Scotland should take around 1,000 migrants fleeing Africa & the Middle East, shadow Home Secretary Yvette Cooper has suggested.
The Labour leadership contender called for 10,000 places to be offered across the UK.
The extra beds would help ease the worst humanitarian crisis to affect Europe since World War Two, she said.
According to the United Nations around 330,000 people have tried to cross the Mediterranean in the last eight months, and at least 2,600 of them have died.
Many are fleeing war and persecution in countries like Syria.
Ms Cooper's call followed angry scenes in Hungary. Rail services were suspended as police tried to stop migrants travelling on to Germany from a main railway station in Budapest.
The German Government, which expects to receive around 800,000 asylum applications this year, has called for the influx of refugees to be spread out more equally across European countries.
A spokesman for the Scottish Government said that Scottish ministers had already made clear that they would accept a "fair share" of asylum seekers coming to the UK.
Making her call, Ms Cooper also hit out at the Conservatives, accusing David Cameron and his government of “cowardice” on the issue.
Ministers were fearful of negative headlines, she said, “stuck in the troubled politics of immigration when this is about asylum”.
Last week Ms Cooper attacked the Prime Minister David Cameron for what she said was his government's policy of conflating asylum and immigration.
The Scottish and Welsh Governments, along with councils across England, should band together to help solve the crisis, she said.
She said it should be up to local representatives to decide how many families they could take.
But with almost one in 10 of the UK's population Scotland could be expected to accept around 1,000 people if the final tally reached 10,000.
Mr Cooper told an invited audience: “We can’t carry on like this. It’s immoral, its cowardly.”
"It’s time for us to do more.
"Yes the politics are difficult, but not if we do this together.
"It's time for the Government to pull together an urgent national conference to work with communities and councils to see how many places we can offer to refugees from Syria and the Mediterranean.
"Time to ask cities, towns, communities how much they each can do to help
"If every city took 10 refugee families, if every London borough took 10 families, if every county council took 10 families, if Scotland, Wales and every English region played their part, then in a month we'd have nearly 10,000 more places for vulnerable refugees fleeing danger, seeking safety.10,000 instead of 200."
She contrasted the current response to what was happening in Europe to events in the 1930s, when the UK took in 80,000 people fleeing the Nazis.
So far the UK has accepted only 200 asylum seekers.
Iceland’s government is aiming to raise its refugee quote after more than 11,000 citizens offered to take Syrian refugees into their homes. The Government had earlier said only 50 would be accepted this year.
Author and professor Bryndis Bjorgvinsdottir launched a Facebook campaign at the weekend calling on the government to up its intake.
Ms Cooper said: "I’m asking everyone to do their bit however large or small.
"The truth is I’m not really asking very much at all. I’m asking us to do something we’ve done before, something we will do again - to help those who need us.”
She admitted that some who came to the UK would “undoubtedly have no asylum claim and should return or follow normal immigration rules”.
But, she added, "be in no doubt – very many of those travelling are refugees from conflict and persecution, especially from Syria, Libya and Eritrea where violence, oppression, instability and persecution have driven millions from their homes”.
Downing Street said: "The UK has a proud history of providing refuge to those in need and we should continue to do so, while also tackling illegal economic migration."
Humza Yousaf, the Scottish Government's Europe minister, said: “The Scottish Government has repeatedly urged the UK Government to take more refugees and we are very happy for Scotland to play her role and take a fair share.
"I remain convinced that Scotland and the UK, and all our friends and neighbours across the EU, have a moral obligation to provide humanitarian assistance to those who need it. This is not about politics but about our common humanity."
Official figures released last week show that net migration to the UK had reached record levels.
The statistics were embarrassing for Mr Cameron who has stated publicly that he wants to drastically reduce the numbers coming to the UK, to the tens of thousands a year.
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