Short answer
He never did. Many Christians say that Jesus' blood on the cross ended the Law of Moses. Yet in the Gospels' own account, the risen Jesus never said so. After the resurrection he told his disciples that "all things must be fulfilled, which were written in the law of Moses". His last command was to teach people "to observe all things whatsoever I have commanded you", and he had taught them to keep even the least of the commandments. At the Last Supper he said his blood was shed "for the remission of sins", not to end the Law. After he had gone, Peter still said he had never eaten anything unclean, and thousands of believers were "all zealous of the law". The idea that the cross ended the Law comes from Paul's letters, not from Jesus. Islam's answer: Jesus came to confirm the Law, the Qur'an says he was not crucified, and only God (﷾) changes His Law, through a prophet.
Full explanation
What many Christians claim
The Law of Moses is the set of commandments God (﷾) gave to Moses: the Sabbath, circumcision, the food laws and the rest. Many Christians say Jesus' death on the cross ended it. They quote Paul, a missionary of the first century who never met Jesus in his lifetime. Paul says Christ "abolished in his flesh the enmity, even the law of commandments contained in ordinances". He also speaks of the ordinances being blotted out, "nailing it to his cross". But these are Paul's words. The question is what Jesus himself said.
“Having abolished in his flesh the enmity, even the law of commandments contained in ordinances; for to make in himself of twain one new man, so making peace;”
“Blotting out the handwriting of ordinances that was against us, which was contrary to us, and took it out of the way, nailing it to his cross;”
After the resurrection, Jesus pointed back to the Law
In the Gospels' own account, Jesus rose and was seen by his disciples for forty days, "speaking of the things pertaining to the kingdom of God". In all that time, not one word ends the Law. He told them instead: "all things must be fulfilled, which were written in the law of Moses". He did not say they had been fulfilled. He said they must be. His last command was to teach all nations "to observe all things whatsoever I have commanded you". What he had commanded included keeping even the least of the commandments. If his blood had ended the Law, these forty days were the time to say so. He never did.
“To whom also he shewed himself alive after his passion by many infallible proofs, being seen of them forty days, and speaking of the things pertaining to the kingdom of God:”
“And he said unto them, These are the words which I spake unto you, while I was yet with you, that all things must be fulfilled, which were written in the law of Moses, and in the prophets, and in the psalms, concerning me.”
“Teaching them to observe all things whatsoever I have commanded you: and, lo, I am with you alway, even unto the end of the world. Amen.”
“Whosoever therefore shall break one of these least commandments, and shall teach men so, he shall be called the least in the kingdom of heaven: but whosoever shall do and teach them, the same shall be called great in the kingdom of heaven.”
His blood was for sins, not for the Law
At the Last Supper, Jesus said of the cup: "this is my blood of the new testament, which is shed for many for the remission of sins". The remission of sins is their forgiveness. He did not say his blood would end the Law. Earlier he had said the opposite: "Think not that I am come to destroy the law". He added that not one jot would pass from the Law "Till heaven and earth pass". Heaven and earth have not passed.
“For this is my blood of the new testament, which is shed for many for the remission of sins.”
“Think not that I am come to destroy the law, or the prophets: I am not come to destroy, but to fulfil.”
“For verily I say unto you, Till heaven and earth pass, one jot or one tittle shall in no wise pass from the law, till all be fulfilled.”
His disciples kept the Law after the cross
The men who had walked with Jesus and seen him risen still kept the Law. Some years after the cross, Peter said: "I have never eaten any thing that is common or unclean." Christians often say Peter's vision of unclean animals ended the food laws. But Peter himself explains it: "God hath shewed me that I should not call any man common or unclean." The vision was about people, not food. Believers from the Pharisees still said converts must be circumcised and keep the Law of Moses. The elders in Jerusalem told Paul that thousands of believers "are all zealous of the law". If the cross had ended the Law, the people closest to Jesus did not know it.
“But Peter said, Not so, Lord; for I have never eaten any thing that is common or unclean.”
“And he said unto them, Ye know how that it is an unlawful thing for a man that is a Jew to keep company, or come unto one of another nation; but God hath shewed me that I should not call any man common or unclean.”
“But there rose up certain of the sect of the Pharisees which believed, saying, That it was needful to circumcise them, and to command them to keep the law of Moses.”
“And when they heard it, they glorified the Lord, and said unto him, Thou seest, brother, how many thousands of Jews there are which believe; and they are all zealous of the law:”
The idea came from Paul
The words that the Law was abolished, or nailed to the cross, are Paul's. Paul also wrote that Christ is "the end of the law". Jesus never said any of this. Even the letter to the Hebrews, written years after the cross, calls the first covenant "ready to vanish away": still there, not gone. And Paul himself had Timothy, a young disciple, circumcised after the cross. Christians are asked to believe that the cross ended the Law on Paul's word, not on Jesus' own.
“Having abolished in his flesh the enmity, even the law of commandments contained in ordinances; for to make in himself of twain one new man, so making peace;”
“Blotting out the handwriting of ordinances that was against us, which was contrary to us, and took it out of the way, nailing it to his cross;”
“For Christ is the end of the law for righteousness to every one that believeth.”
“In that he saith, A new covenant, he hath made the first old. Now that which decayeth and waxeth old is ready to vanish away.”
“Him would Paul have to go forth with him; and took and circumcised him because of the Jews which were in those quarters: for they knew all that his father was a Greek.”
Islam's answer
The Qur'an says Jesus was not killed or crucified, so no death of his ended anything. It says he came "to attest the Law which was before me", and to make lawful part of what had been forbidden. So the Law was not ended by a death. Only God (﷾) changes His Law, and only through a prophet. Through the Prophet Muhammad (ﷺ), God (﷾) lifted the heavy burdens that had been laid on the Children of Israel.
“That they said (in boast), "We killed Christ Jesus the son of Mary, the Messenger of Allah";- but they killed him not, nor crucified him, but so it was made to appear to them, and those who differ therein are full of doubts, with no (certain) knowledge, but only conjecture to follow, for of a surety they killed him not:-”
“"'(I have come to you), to attest the Law which was before me. And to make lawful to you part of what was (Before) forbidden to you; I have come to you with a Sign from your Lord. So fear Allah, and obey me.”
“"Those who follow the messenger, the unlettered Prophet, whom they find mentioned in their own (scriptures),- in the law and the Gospel;- for he commands them what is just and forbids them what is evil; he allows them as lawful what is good (and pure) and prohibits them from what is bad (and impure); He releases them from their heavy burdens and from the yokes that are upon them. So it is those who believe in him, honour him, help him, and follow the light which is sent down with him,- it is they who will prosper."”
Perspectives
The cross ended the Law
Many Christians say Jesus' death on the cross fulfilled the Law and ended its rules, so that believers are no longer bound by the Law of Moses.
Paul says Christ abolished the law of commandments in his flesh and nailed the ordinances to his cross.
Rebuttal
These are Paul's words, not Jesus'. After the cross, the risen Jesus said all things written in the law of Moses must be fulfilled, and told his followers to teach others to observe all he had commanded. Paul himself had Timothy circumcised after the cross.
Jesus said the Law would stand till all was fulfilled, and he fulfilled it on the cross.
Rebuttal
The same verse says not one jot will pass from the Law till heaven and earth pass, and they have not passed. After the cross, the risen Jesus still said that all things written in the law "must be fulfilled", as something still to come.
Peter's vision showed that the food laws had ended.
Rebuttal
Peter explains his own vision: God (﷾) had shown him not to call any man common or unclean. It was about people, not food. And in all the years since the cross, he had never eaten anything unclean.
The Islamic perspective
Jesus confirmed the Law of Moses and never ended it. The Qur'an says he was not crucified. The idea that the cross ended the Law comes from Paul. Only God (﷾) changes His Law, through a prophet, as He did through the Prophet Muhammad (ﷺ).
After the resurrection, Jesus said all things written in the law of Moses must be fulfilled.
His last command was to teach people to observe all he had commanded.
He said his blood was shed for the remission of sins, not to end the Law.
Peter and thousands of believers kept the Law years after the cross.
The Qur'an says Jesus came to confirm the Law, and that he was not crucified.