The term Islamic should be dropped when referring to terrorists in a bid to foster better relations between the West and Islam, Lord Carey says.
Lord Carey urged Muslims to denounce terrorism more often
The former Archbishop of Canterbury said removing the word would "deprive a terrorist of his religious legitimacy".
It would also send a clear message to "the average Muslim" that they were not being blamed for terrorist attacks.
His comments come after Muslim leaders expressed concern about a growing gulf between the Islamic world and the West.
Malaysian Prime Minister Abdullah Ahmad Badawi has warned that linking international terrorism and Islam was damaging.
"There is an urgent need to stop tarnishing the Muslim world by unfair stereotypes," he told the United Nations this week.
Pakistan President Pervez Musharraf has also said there is an "iron curtain" falling between the
Islamic world and the West.
However, Lord Carey said that while there was a divide, he wanted to resist using such a serious phrase as "iron curtain".
"There is a lot of hope in the situation, but I certainly want to say the situation is serious.
"We must do more about it, and it's a question of everyone pulling together," he told BBC Radio 4's Today programme.
He had begun a personal campaign "to challenge anyone who talks about Islamic terrorists", Lord Carey added.
"I think we have to drop the word Islamic because in so doing we deprive the terrorist of his religious legitimacy.
"He wants religious justification for his evil deeds, and we shouldn't give it to him," Lord Carey said.
"And second, by dropping Islamic before terrorist we are taking a lot of pressure off the average Muslim who simply doesn't want to be portrayed as a fellow murderer."
He said he accepted that the problems in the Middle East and Iraq had to be addressed, "but it would help the building of bridges if we helped the average Muslim to understand that we are not blaming Islam for this".
"We're blaming that tiny, tiny minority of people who are using Islam as a weapon to get their own back against the West and to undermine all we're trying to do."
Lord Carey reiterated his call for Muslims to denounce terrorism more often.
"Terrorists are very evil people and I want to hear Muslims say that more and more," he said.