David Cameron will face demands to do more to help refugees after a pledge to resettle up to 20,000 in the UK over five years was dismissed by the Archbishop of Canterbury as "a very slim response".
Labour has forced an emergency Commons debate on the mounting crisis and is demanding a commitment that far more than 4,000 will arrive this year and that Britain should also take in a share of those already in Europe.
The Prime Minister, effectively forced to reverse opposition to accepting more people after a photo of a drowned migrant child galvanised public opinion, told MPs the new scheme would meet the country's "moral responsibility".
But he insisted it would involve only vulnerable refugees from camps in the region, and not those who have entered Europe in their thousands over recent months - in an attempt to dissuade others from making the perilous journey.
The UK, Mr Cameron said, would not take part in a planned European Commission request for EU member states to resettle a share of the 160,000 migrants who have already arrived in the continent.
The new refugees will be offered five-year humanitarian visas and the cost of their first year in Britain will be met from the Government's aid budget.
The archbishop, the Most Rev Justin Welby said the number would have to rise unless conditions in the camps was dealt with and warned the problem "can only morally and credibly be dealt with by widespread European collaboration".
A ComRes poll for BBC2's Newsnight found 40% of Britons back a rise in the number of refugees admitted, against 31% who said fewer should be allowed in and 26% who thought numbers should remain as they are.
Pressure to admit more Syrians has grown since the publication of photographs of three-year-old Aylan Kurdi, who drowned with his mother and brother trying to cross from Turkey to Greece by boat.
Those who had seen the pictures of Aylan's body lying on a Turkish beach were significantly more likely to think Britain should accept more refugees.
Aid agencies welcomed the Government's change of heart but said the numbers allowed to settle in the UK must be kept under review and urged the acceptance of some of those already in Europe.
Shadow home secretary Yvette Cooper, who persuaded Commons Speaker John Bercow to allow today's emergency debate, said: "Twenty thousand over five years could mean 4,000 a year.
"I would urge the Prime Minister to reconsider and to look at what more we are able to do with councils, with communities across the country who have come forward asking to help and do more."
The Labour leadership candidate - who is among politicians and celebrities who have expressed willing to put refugees up in their own homes - dismissed the argument for restricting the scheme to those still in regional camps.
"He (the PM) has said he does not want to encourage people to travel - I would say to him they are travelling already, they are not waiting for a response from the British Government."
International Development Secretary Justine Greening told BBC2's Newsnight it was "impossible to say there was this one moment that changed policy" and that the Government was showing flexibility in the face of an evolving situation.
She said Britain could be "really proud" of its help to the Syrian people since the start of the crisis - as the second-largest bilateral donor of humanitarian aid.