Short answer
No. In Islam every person turns to God (﷾) directly, with no priest, saint or go-between. The Qur'an says God (﷾) is near and answers everyone who calls on Him. It says He is nearer to a person than his own jugular vein, the large vein in the neck. A Muslim who sins confesses to God (﷾) alone, regrets it, and turns back to Him. The door of repentance stays open until death. The Prophet (ﷺ) taught that calling on God (﷾) is itself worship, so it belongs to God (﷾) alone. He even told his own daughter, Fatima, that he could not help her at all against Allah (﷾). An imam leads the prayer and teaches, but he hears no confession and grants no pardon. Islam's answer is that God (﷾) Himself forgives.
Full explanation
God (﷾) is near and answers the one who calls
The Qur'an states that God (﷾) is close. He hears every person who calls on Him, and He answers. He is nearer to a person than his jugular vein, and He knows what a person's own soul whispers. So no one has to carry a prayer to Him. Nothing about His servant is hidden from Him.
“When My servants ask thee concerning Me, I am indeed close (to them): I listen to the prayer of every suppliant when he calleth on Me: Let them also, with a will, Listen to My call, and believe in Me: That they may walk in the right way.”
“It was We Who created man, and We know what dark suggestions his soul makes to him: for We are nearer to him than (his) jugular vein.”
“And your Lord says: "Call on Me; I will answer your (Prayer): but those who are too arrogant to serve Me will surely find themselves in Hell - in humiliation!"”
Repentance goes straight to God (﷾)
The first human sin in the Qur'an's account is forgiven with no go-between and no sacrifice. Adam and his wife blamed no one. Together they said to their Lord that they had wronged themselves, and God (﷾) turned to Adam in mercy. The same door is open to every person until death. The Qur'an tells even those who have sinned heavily not to despair. It also says that good deeds wipe away bad ones.
“They said: "Our Lord! We have wronged our own souls: If thou forgive us not and bestow not upon us Thy Mercy, we shall certainly be lost."”
“Then learnt Adam from his Lord words of inspiration, and his Lord Turned towards him; for He is Oft-Returning, Most Merciful.”
“Say: "O my Servants who have transgressed against their souls! Despair not of the Mercy of Allah: for Allah forgives all sins: for He is Oft-Forgiving, Most Merciful.”
“Of no effect is the repentance of those who continue to do evil, until death faces one of them, and he says, "Now have I repented indeed;" nor of those who die rejecting Faith: for them have We prepared a punishment most grievous.”
“And establish regular prayers at the two ends of the day and at the approaches of the night: For those things, that are good remove those that are evil: Be that the word of remembrance to those who remember (their Lord):”
A mercy with no go-between
The Prophet (ﷺ) taught that God (﷾) kept ninety-nine parts of His mercy for Himself and sent one part to earth. He taught that God (﷾) comes running to the servant who walks toward Him. A good deed is written down ten to seven hundred times over, and a bad deed only once. So no priest or church can grant pardon on God's (﷾) behalf. Even good deeds do not earn Paradise on their own. A person enters it by God's (﷾) mercy, which he asks of God (﷾) Himself.
Abu Hurayra heard the Prophet (ﷺ) say that Allah divided mercy into a hundred parts, kept ninety-nine with Himself and sent one part down to earth; from that one part all creatures show mercy to each other, so that a mare lifts her hoof from her foal for fear of treading on it. Also in Sahih Muslim 2752.
The Prophet (ﷺ) reports that Allah says: I am as My servant thinks of Me, and I am with him when he remembers Me; if he comes a hand-span nearer to Me, I come an arm's length nearer to him, and if he comes to Me walking, I go to him running. Also in Sahih Muslim 2675.
Ibn Abbas reports that the Prophet (ﷺ), telling what his Lord said, taught: a good deed intended but not done is written as one full good deed; if it is done, it is written as ten to seven hundred times over, or more; a bad deed intended but not done is written as a full good deed; if it is done, it is written as one bad deed only. Also in Sahih Muslim 131.
Abu Hurayra reports that the Prophet (ﷺ) said no one's deeds will save him. Asked whether that included him, he said: not even me, unless Allah covers me with His mercy. He then told them to do good deeds properly, sincerely and in moderation.
Calling on God (﷾) is worship, so it goes to God (﷾) alone
The Prophet (ﷺ) said that supplication (du'a, which means calling on God (﷾)) is itself worship. In every prayer a Muslim says to God (﷾), "Thee do we worship, and Thine aid we seek." So a prayer sent to a saint or an angel gives part of worship to someone other than God (﷾). The Qur'an says those called on besides Allah (﷾) are servants like the people calling them. It also rejects the old excuse that such helpers only bring people nearer to Allah (﷾).
Al-Nu'man ibn Bashir reports that the Prophet (ﷺ) said that supplication is itself worship, and then recited the verse in which God says: call on Me and I will answer you (Qur'an 40:60).
“Thee do we worship, and Thine aid we seek.”
“Verily those whom ye call upon besides Allah are servants like unto you: Call upon them, and let them listen to your prayer, if ye are (indeed) truthful!”
“Is it not to Allah that sincere devotion is due? But those who take for protectors other than Allah (say): "We only serve them in order that they may bring us nearer to Allah." Truly Allah will judge between them in that wherein they differ. But Allah guides not such as are false and ungrateful.”
Not even the Prophet (ﷺ) can grant pardon
The Qur'an tells the Prophet (ﷺ) to say that he has no power to bring good or harm even to himself. When he warned his own family, he told his daughter Fatima that he could not help her at all against Allah (﷾). Islam does teach that on the Day of Judgement some will intercede (plead for others), but only those God (﷾) permits. No one in this life stands between a person and his Lord.
“Say: "I have no power over any good or harm to myself except as Allah willeth. If I had knowledge of the unseen, I should have multiplied all good, and no evil should have touched me: I am but a warner, and a bringer of glad tidings to those who have faith."”
Abu Hurayra reports that when the verse "warn your nearest kinsmen" (Qur'an 26:214) came down, the Prophet (ﷺ) called out to Quraysh, to his uncle al-Abbas, his aunt Safiyya and his daughter Fatima, telling each that he could not help them at all against Allah; Fatima could ask him for whatever she liked, but he could not help her at all against Allah.
“On that Day shall no intercession avail except for those for whom permission has been granted by (Allah) Most Gracious and whose word is acceptable to Him.”
What Christians hold
Now the Christian view. The Catholic and Orthodox churches teach that a priest forgives sins in the sacrament of confession, a church rite. They say Christ gave this authority to the apostles, his chosen disciples, and they read John 20:23 this way. Most Protestant churches do not require confession to a priest. But all of them hold that Christ is the one mediator (go-between) between God (﷾) and people. They hold that sin is forgiven only through his sacrifice.
“Whose soever sins ye remit, they are remitted unto them; and whose soever sins ye retain, they are retained.”
“For there is one God, and one mediator between God and men, the man Christ Jesus;”
What Jesus taught about prayer and forgiveness
Jesus' own teaching points the other way. In the Gospels he sends people to God (﷾) directly. He told them to pray to the Father in private, and to ask the Father themselves to forgive them. In his parable (a story with a lesson) of the lost son, the father runs to meet his son and forgives him with no go-between. The tax collector who asked God (﷾) for mercy in his own words went home justified (right with God (﷾)).
“But thou, when thou prayest, enter into thy closet, and when thou hast shut thy door, pray to thy Father which is in secret; and thy Father which seeth in secret shall reward thee openly.”
“And forgive us our debts, as we forgive our debtors.”
“And he arose, and came to his father. But when he was yet a great way off, his father saw him, and had compassion, and ran, and fell on his neck, and kissed him.”
“And the publican, standing afar off, would not lift up so much as his eyes unto heaven, but smote upon his breast, saying, God be merciful to me a sinner. I tell you, this man went down to his house justified rather than the other: for every one that exalteth himself shall be abased; and he that humbleth himself shall be exalted.”
Verse by verse
1 Timothy 2:5 — First Epistle to Timothy, chapter 2, verse 5
“For there is one God, and one mediator between God and men, the man Christ Jesus;”
Cited for
Christians read this as teaching that no one reaches God except through Christ, who is both God and man.
The response
The verse itself sets "one God" apart from the mediator, and calls the mediator "the man Christ Jesus". And Jesus taught his disciples to pray to the Father in secret and to ask the Father to forgive them.
Where it lands — The verse keeps the one God (﷾) and the man Christ Jesus apart. In the prayer Jesus taught (Matthew 6:9-13), sinners ask the Father for forgiveness without naming any mediator.
John 14:6 — Gospel of John, chapter 14, verse 6
“Jesus saith unto him, I am the way, the truth, and the life: no man cometh unto the Father, but by me.”
Cited for
Jesus said no one comes to the Father except through him, so every prayer must pass through Christ.
The response
Jesus is the way as the messenger whose teaching leads to God (﷾). In the same Gospel he says eternal life is to know "the only true God, and Jesus Christ, whom thou hast sent". The way he taught was to pray to the Father directly, and his own model prayer names no one in between. Even where John has him say "ask in my name", he adds something. He will not pray the Father for them, because the Father himself loves them (John 16:26-27).
Where it lands — Coming to the Father by Jesus means following the message of the one God (﷾) sent. It does not mean praying to or through him.
John 20:23 — Gospel of John, chapter 20, verse 23
“Whose soever sins ye remit, they are remitted unto them; and whose soever sins ye retain, they are retained.”
Cited for
Catholic and Orthodox Christians read this as Christ giving the apostles, and the priests after them, power to forgive sins in confession.
The response
The verse names no priesthood and no successors, and says nothing about confessing to another person. In Luke's Gospel, the tax collector spoke to God (﷾) alone and went home justified. The lost son's father ran to meet him while he was still far off.
Where it lands — Nothing in the verse requires a sinner to go through a priest, and Jesus' own teaching shows forgiveness asked of God (﷾) directly.
Perspectives
Christian
Forgiveness comes through Christ, the one mediator. Catholic and Orthodox Christians also confess to a priest, who pardons in Christ's name. Most Protestants confess to God directly through Christ.
There is one mediator between God and people, Christ Jesus, and forgiveness comes through him.
Rebuttal
The verse does speak of one mediator. But it sets "one God" apart from "the man Christ Jesus". And the prayer Jesus taught asks the Father to forgive, naming no sacrifice and no one in between.
In John 20:23 Jesus gives the apostles authority to forgive or retain sins. Catholic and Orthodox churches hold that it passes to their priests.
Rebuttal
The verse does speak of forgiving sins. But it names no priesthood and no successors, and it says nothing about confessing to another person. In Jesus' own story the tax collector asked God (﷾) alone and went home justified. The Qur'an asks, "who can forgive sins except Allah?"
The Islamic perspective
Every person stands before God (﷾) directly. He hears every caller, forgives whoever turns to Him sincerely, and needs no priest, saint or sacrifice. The Prophet (ﷺ) taught people to ask God (﷾) alone.
The Qur'an states that God (﷾) is near and answers every caller. He is nearer to a person than his jugular vein.
Supplication is worship, so praying to or through anyone besides God (﷾) gives worship to a creature.
The Qur'an rejects the claim that other beings are needed to bring people nearer to God (﷾).
Adam and his wife repented to God (﷾) in their own words. God (﷾) forgave Adam with no mediator and no sacrifice.
The door of repentance is open to every person until death, however great the sin. And good deeds wipe away bad ones.
Sahih (sound) hadith are reports of the Prophet's (ﷺ) words. They describe God's (﷾) mercy toward the one who turns to Him. They speak of ninety-nine parts of mercy kept with Him, of Him running to meet the servant, and of good deeds multiplied.
The Prophet (ﷺ) told his own daughter he could not help her against Allah (﷾). The Qur'an has him say he has no power even over his own good or harm.
Intercession (pleading for others) on the Day of Judgement belongs only to those God (﷾) permits. It is not a gate a person must pass through in this life.
Jesus taught people to pray to the Father directly and to ask Him themselves for forgiveness.