The Prime Minister caved after a campaign launched by Citizens UK called on him to break a deadlock between central and local government that would help hundreds fleeing destitution enter Britain before temperatures in refugee camps plummet.
Six children reportedly perished in emergency shelters housing displaced Syrians last year because of weather conditions.
Speaking in the Commons on Monday, Cameron for the first time put a figure on the number of Syrians he would relocate before December 31.
Conditions in a Syrian refugee camp last Winter
"We want to see 1,000 refugees brought to Britain by Christmas and we’ll report on that after Christmas to tell you how we have done," he said.
The Prime Minister also rebuked 84 Church of England bishops, who on Sunday wrote an open letter to him urging the UK to increase the number of migrants it would accept over the next five years from 20,000 to 50,000.
Those senior religious figures were "wrong", Cameron claimed, saying: "No-one has more respect for the bishops than me, but on this occasion, yes, I think they’re wrong and I’ll say so very frankly."
He called on the bishops to make a "very clear statement" that his Government was ensuring Britain "fulfilled our moral obligations".
The former shadow home secretary's criticism came as her opposite number in Government, Richard Harrington, refused to confirm how many Syrian refugees had already come to the UK - despite repeated questioning by a group of select committee MPs.