Dr John Sentamu said that like others who speak out on the subject, he risked being accused of Islamophobia.
He said: "My plea to all Muslims in this country is the words of Jesus Christ, who to you is a prophet and to me a saviour." The archbishop then quoted the Gospel of Matthew: "You have heard that it was said, you shall love your neighbour and hate your enemy.
"I say to you, love your enemies and pray for those who persecute you. If you love those who love you, what reward do you have?"
The call comes at a time of high tensions over terrorism and the measures used to fight it.
Muslim leaders have been critical of security techniques such as profiling, in which people who are deemed to look most like terrorists are singled out for questioning.
Ugandan-born Dr Sentamu, who became the CofE's first black archbishop last year, has made a strong impression with calls for the return of Christian values to British life and a rejection of multiculturalism.
He said it was unhelpful to call Muslim terrorists Islamic fundamentalists or fascists as these were Christian and political terms that "further alienate those who commit these crimes".
He said they should be called Salafi Jihadists, after the Islamic concept of struggle, which has been bent into the pursuit of murder and mass destruction by members of the Salafi movement.
The Salafi - or Wahabi - branch of Islam, which is dominant in Saudi Arabia, has many peaceful followers who aim to return to the purity of early Islam.
Dr Sentamu said: "For the modern day Salafi Jihadist who defines themselves through acts of mass destruction and terror, Jihad has taken on a whole new meaning.
"There is always a danger when making comments about Jihadists that the charge of Islamophobia follows close behind.
"So let me be clear. I am not by any means talking about all of Islam or all Muslims here."
He said Christians should recognise that one of the biggest contributions of Muslims in Britain had been their denial of the idea that faith should be marginalised.
Dr Sentamu added: "It has often been Muslims who have joined Christians in refusing to accept the creeping secularisation that would replace Christmas with Winterval and remove references to faith from public noticeboards for fear of causing offence.
"It is both my view and my experience that most British Muslims do not feel threatened by our Christian moral foundations but by the cynicism of the secular culture that denies its own foundations."
The Muslim Council of Britain, the Islamic group with closest links to the government, said it could not accept the plea for Muslims to love their enemies.
Spokesman Inayat Bunglawala said: "Just as we could not call on Jews to turn the other cheek when faced with anti-Semitism, it cannot be right that we are asked to tolerate anti-Muslim prejudice.
"We should have a zero-tolerance policy towards all forms of prejudice, be it anti-Jewish, anti-Muslim or anti-Christian. But we cannot just turn the other cheek.
"By the same token we cannot take the law into our own hands. The right way is for Muslims to set an example by their own behaviour."
