Taking in more refugees from Syria and other war-torn countries could help David Cameron secure European Union reforms, Labour leadership candidate Andy Burnham suggested.
Mr Burnham said Britain was failing to "play our part" in dealing with a dramatic rise in numbers seeking a safe haven in Europe.
It comes after the discovery of 71 bodies in a truck in Austria heightened criticism of the continent's response to people smuggling.
He says that playing our role in the crisis make other countries more likely to agree to wider changes around benefits and housing being sought by the Prime Minister as part of his renegotiation of EU membership.
Mr Cameron is facing competing political pressures to bring down record levels of net immigration into Britain and to help deal with the refugee crisis.
We can't just say it is everyone else's problem and not ours, we have got to play our part. I think if we were to do that I think we might get more of what we want to negotiate on EU migration.
Elsewhere, the Shadow home secretary Yvette Cooper- and fellow leadership contender - said including refugees and asylum seekers in the Government's target to reduce net migration to the tens of thousands was "immoral".
The Government should admit its mistake, scrap the target, and replace it with a more sensible system that completely separates immigration and asylum.
Ms Cooper promises to reform the asylum system by ending indefinite detention and stopping the practice of repatriation of children when they turn 18.
Labour leadership frontrunner Jeremy Corbyn said the Government needed to look at the issue "with renewed humanity" and stop treating migrants and those fleeing persecution "as criminals".