The Archbishop of York says if no action is taken a genocide could be committed by Islamic State (IS) terrorists.
He described the group as 'bloodthirsty' as it continues to advance across Iraq forcing thousands of Christians to leave their homes.
In the past IS has issued ultimatums to Christians to leave, pay a tax or be killed.
Speaking to the BBC's Sunday Morning Live programme he said the UK government had to follow the lead of other countries, like France, and offer asylum to the persecuted.
"Please act quickly, because we may end up with a Rwanda... where people are really killed in huge, huge numbers," he said.
The Archbishop stressed that he did not want to embarrass the Prime Minister but it was important a decision was made fast.
He said: "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."
Archbishop Sentamu has just finished a week-long prayer vigil, praying on the hour every hour, between 6am and 6pm.