David Miliband has joined calls for the UK to take more refugees - suggesting Britain should be committing to help up to 25,000 a year - four times the original pledge.
Last year ministers agreed to take in 20,000 people driven from the war-torn country by 2020 following a public outcry over the fate of those attempting the perilous journey across the Mediterranean.
The former Foreign Secretary said this equates to just six refugees per parliamentary constituency over the five-year period - a figure which would not overwhelm his former seat of South Shields.
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Ahead of the UN Summit on refugees and migrants in New York beginning on Monday, Mr Miliband said there "needs to be a clear commitment" from the richer countries to tackle the issue.
Speaking on Sky News's Murnaghan programme he said: "I think there is quite a lot of scope for Theresa May to come to the UN and to the Obama summit on Tuesday and say 'look, the UK has a really good record on international overseas aid'.
"We are a leader, the UK is a leader, through the Department for International Development, on global humanitarian help. But we can also make a greater contribution beyond the six refugees per parliamentary constituency.
"Frankly, the UK should be saying we will take 20,000 or 25,000 a year, so four times the current level, 25 refugees per parliamentary constituency rather than just six because countries like Canada are already doing that."
The current president of the International Rescue Committee added: "I think the UK could do more on the refugee resettlement side to match the, frankly, exemplary performance the UK has on international humanitarian aid."
He also said there is a need to deal with the "symptoms of the problem, that is the fleeing refugees", but also the "humanitarian conditions in countries like Lebanon, Jordan, Pakistan" which is "driving" people to seek refuge in Europe.
Labour's refugee taskforce chair Yvette Cooper has also urged Mrs May to meet the Government's pledge to resettle 20,000 Syrian refugees two years early, and then help more.
The former cabinet minister also called for the Prime Minister to resettle 500 lone child refugees before Christmas - ensuring no youngster is left in Calais' "Jungle" camp over the festive period.
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"She must go to this summit to galvanise international support for refugees and show that Britain can and will meet our commitments.
"Right now the decisions Parliament and our country have taken are being mired in red tape and Government foot-dragging.
"Yet all the while lives are at risk. Britain has always done its bit to help those fleeing persecution - we have to live up to those values again now.
"It is shameful that we still haven't welcomed any lone child refugees under the Dubs amendment.
"It is appalling that so many children and teenagers with family in Britain are still stuck in miserable and dangerous conditions in the Calais camp because of bureaucratic delays.
"Surely it is not beyond the wit of two great nations, Britain and France, to end the scandal of Calais."
On Saturday, Solidarity with Refugees who organised the Refugees Welcome march, estimated 10,000 people had taken to the streets of London in a bid to urge the Government to do more to tackle the issue.
Religious leaders, refugees, actors such as Vanessa Redgrave, Douglas Booth and Juliet Stevenson, as well as figures including MP Caroline Lucas, Labour's Lord Alf Dubs and Liberal Democrat campaigner Baroness Sheehan, addressed the crowd.
Solidarity with Refugees director Ros Ereira told the Press Association she hopes the Prime Minister "sets the tone" for what kind of country the UK can be at the summit.
She added: "Hopefully she will want to portray us as an open, tolerant, welcoming society that wants to play an important role on the global stage and lead an appropriate global humanitarian response."
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A Home Office spokeswoman said: "The Government has committed to take in 20,000 Syrian refugees under our Syrian Vulnerable Persons Scheme (VPR) and more than 2,800 have been granted humanitarian protection since the scheme began.
"We have secured all the local authority pledges required to meet this commitment and the hard work across Government involving the devolved administrations and local authorities will continue until we have turned all of these pledges into places and resettled 20,000 people.
"We will manage the flows based on need and in support of the wellbeing of the people and communities involved, rather than rushing to meet arbitrary targets."
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