Expectations are growing that Britain may open its doors to more Syrian refugees, after Prime Minister David Cameron said that the UK's response was "under review".
Urgent discussions are under way in Whitehall on what form any extra help could take, and reports suggested that an announcement could be made within the coming days.
The Guardian suggested that thousands more refugees could be taken from United Nations camps on the Syrian border under a scheme for vulnerable people, while Sky News reported that 4,000 more people could be offered asylum.
Mr Cameron said he was "deeply moved" as a father by shocking pictures of a three-year-old Syrian boy washed up on a beach in Turkey after he, his brother and their mother drowned in an attempt to reach Europe by boat.
The PM promised that the UK would fulfil its "moral responsibilities" amid growing demands for action in response to a crisis which has seen hundreds of thousands of people attempting to enter Europe from north Africa and the Middle East.
Speaking during a visit to County Durham, Mr Cameron told reporters: "As a father, I felt deeply moved by the sight of that young boy on a beach in Turkey.
"Britain is a moral nation and we will fulfil our moral responsibilities."
The Government has declined to join a UN scheme for resettling the most vulnerable refugees, instead setting up its own programme that has admitted around 216 over the past year. Some 5,000 Syrians have been granted asylum in the last four years. Britain has refused to join a EU scheme to resettle migrants arriving in countries like Italy, Greece and Hungary.
By contrast, Germany has accepted 35,000 vulnerable Syrians through the UN scheme, Canada more than 10,000, Australia 5,600 and Switzerland 3,500. European Commission president Jean-Claude Juncker is next week expected to call for EU countries to resettle some 160,000 migrants around the continent.
Mr Cameron stressed that Britain is the second-largest bilateral donor supporting Syrian refugees in the region, with around £900 million of UK money going into food, tents and other aid, and has sent a Royal Navy ship to rescue migrants from drowning in the Mediterranean.
He said: "We are taking thousands of Syrian refugees and we will continue to do that. As I said yesterday, we keep that under review."
Labour leadership candidates taking part in a televised debate on Sky News said the Prime Minister was not doing enough to respond to the mounting crisis.
Jeremy Corbyn said that accepting 4,000 additional refugees "doesn't seem like enough", saying: "We have to hold out the hand of humanity and support and friendship... Every European country should do its best. Germany has shown the way."
Shadow home secretary Yvette Cooper, who has suggested the UK could take 10,000 more refugees, said: "Other countries are doing their best. We have got to do more as well."
Liz Kendall said she was "ashamed" of the "heartless and powerless" approach of the Prime Minister, saying Britain should be taking "something in the tens of thousands."
Andy Burnham - who is calling on the Government to present a plan for debate in the House of Commons on Monday - said the PM should be entering immediate talks with his EU counterparts on a deal to tackle the migration problem.
Liberal Democrat leader Tim Farron said: "I sincerely hope that tonight we are starting to see the Prime Minister taking steps to ensure Britain plays its part in helping more refugees.
"It is embarrassing for the country that the Government has had to be dragged kicking and screaming to do the compassionate thing. But we must wait to see the detail - there can be no half measures, it's high time the UK took a full role in helping desperate people."
Pressure has been mounting on the PM at home and abroad for Britain to do more.
Former foreign office minister Baroness Warsi told the BBC Radio 4 Today programme the UK had to be "prepared to share the burden", and fellow Conservative Chris Heaton-Harris said the UK had "always helped refugees fleeing war zones and we should now".
David Burrowes, Tory MP for Enfield Southgate, told the Press Association: "We should be doing more to provide a voluntary solution for Syrian refugees.
"We are in the hundreds - I said then it is too little, too late - and we are still in that situation where other countries are accepting thousands."
French president Francois Hollande delivered a thinly-veiled swipe at the UK by complaining that some countries were not "shouldering their moral obligations".
"I believe that today what we have done is not enough," he told a press conference in Paris. "There are countries - I am not going to name them here because we are here to work with everybody - and these countries are not shouldering their moral obligations."
European Council president Donald Tusk, seen as an ally of the PM, upped the pressure further by arguing that "all EU members" needed to take their share of refugees.
"Now are times of a major test for all EU members. Therefore I call on all EU leaders to re-double their efforts, when it comes to solidarity with the members who face this unprecedented migratory wave," he told a press conference.
"Accepting more refugees is not the only but an important gesture of real solidarity. Fair distribution of at least 100,000 refugees among the EU states is what we need today."
Former foreign secretary David Miliband, now chief executive of humanitarian charity International Rescue, told BBC Radio 4's PM: "If it's correct that the European Commission is proposing a figure of about 160,000 for the whole of Europe, Britain - as one of the larger countries in Europe - is going to have to be in the tens of thousands."
Asked if this could mean 20-40,000 refugees coming to the UK, Mr Miliband replied: "Exactly."