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.
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 today, 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."
Mr Miliband, 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.