John Sentamu warned the “bloodthirsty” extremists could end up committing genocide as the conflict in Iraq and Syria intensifies.
Prime Minister David Cameron is expected to outline powers to stop would-be terrorists going abroad during a statement in the Commons today.
Archbishop Sentamu said he did not want to embarrass Mr Cameron, but he thought the UK needed to follow the lead of other countries and do more about asylum.
Speaking on BBC One’s Sunday Morning Live programme yesterday, he said: “Please act quickly, because we may end up with a Rwanda… where people are really killed in huge, huge numbers.
“They’ve already shown their capacity to be bloodthirsty. The beheading should tell us that they are a ruthless group of people, and somehow they’ve got to be stopped. And if you don’t stop them, you may end up with a genocide.”
The Archbishop said the world needed to show it would not stand for the atrocities carried out by IS extremists, who he said were doomed to failure.
He has been holding a week-long prayer vigil, praying on the hour every hour, from 6am to 6pm this week.
The UK faces growing pressure to tackle the terror threat following US air strikes on IS positions in the besieged Iraqi town of Amerli on Saturday.
It has so far granted asylum to over 3,000 Syrians already in the UK, and to at least 50 of the refugees currently in camps in the Middle East after fleeing areas taken over by IS.