Germany told its European partners they must take in more refugees on Monday as it struggles to cope with record numbers of asylum seekers and as police in Hungary used pepper spray on migrants who broke out of a reception centre at the border.

Chancellor Angela Merkel, speaking after a weekend in which 20,000 migrants entered Germany from Hungary by train, bus and on foot, described the influx as "breathtaking" and tried to reassure the country the crisis was manageable.

Dramatic images from last week, especially a photograph of a Syrian toddler drowned on a Turkish beach, have created new political pressure to open doors, even in countries that argued previously that taking in too many migrants could make the problem worse by encouraging others to make dangerous voyages.

"I am happy that Germany has become a country that many people outside of Germany now associate with hope," she said at a news conference in Berlin.

But she and her vice chancellor, Sigmar Gabriel, coupled their message of optimism with a warning to EU partners who have resisted a push from Berlin, Paris and Brussels to agree to quotas for refugees flowing in mainly from Syria, Iraq and Afghanistan.

"What isn't acceptable in my view is that some people are saying this has nothing to do with them," Merkel said. "This won't work in the long run. There will be consequences although we don't want that."

Gabriel said that if countries in eastern Europe and elsewhere continued to resist accepting their fair share of refugees, the bloc's open border regime, known as Schengen, would be at risk.

"This would be a dramatic political blow for Europe, but also a heavy economic blow, also for those countries that are saying they don't want to help now," he said.

At Roszke, on Hungary's border with Serbia, around 300 migrants broke through a cordon around a reception camp and set off down the wrong side of the motorway towards the capital Budapest, Reuters witnesses said.

Police were unable to prevent their escape despite using pepper spray as migrants scuffled with officers.

Only months after Europe narrowly averted a Greek exit from the euro zone, the refugee have emerged as the bloc's biggest challenge.

Greece asked the European Union for aid on Monday to prevent it being overwhelmed by refugees, as a minister said arrivals on Lesbos had swollen to three times as many as the island could handle.

The crisis also spilled into Denmark as some 800 people entered the country from Germany and tried to head to Sweden while politicians argued about Copenhagen's immigration policies.

Main entry points

European Commission President Jean-Claude Juncker is due to unveil new proposals on Wednesday on how to distribute refugees among member states.

An EU source told Reuters that under Juncker's plan, Germany would take on more than 40,000 and France 30,000 of the 160,000 asylum seekers the Commission says need to be relocated from Italy, Greece and Hungary, the main entry points to the EU for refugees arriving by sea and land.

The 160,000 that Juncker wants to redistribute within the EU are just a fraction of the hundreds of thousands of refugees and economic migrants from Asia, Africa and the Middle East who have reached Europe this year on leaky boats across the Mediterranean or over land through the Balkan peninsula. Many have died en route.

Germany has announced it is letting Syrians seek asylum regardless of where they enter the EU, suspending normal rules and accelerating a flow of migrants north and west from the edges of the bloc.

Just last month, more than 100,000 asylum seekers reached Germany, which is preparing for 800,000 this year, around one per cent of its population, a move with little precedent for a large Western country.

France said it would take in up to 1,000 migrants currently in Germany as a matter of urgency, before the adoption of the European Commission plan.

Britain would resettle 20,000 refugees from Syria over the next five years, Prime Minister David Cameron announced, responding to a growing public clamour for his government to do more to help.

Some rights groups have criticised the United States for not doing more to help. A White House spokesman said the Obama administration was "actively considering a range of approaches to be more responsive to the global refugee crisis, including with regard to refugee resettlement".

Pope Francis called over the weekend for Christian communities across the continent to offer sanctuary.

Hungary's prime minister, Viktor Orban, a right-wing populist whose hard line during the crisis has drawn both praise and criticism, reiterated his opposition to quotas on Monday, calling this debate premature. Juncker's proposal would exempt the main entry countries Hungary, Greece and Italy from taking relocated refugees.

Hungary's defence minister, Hende Csaba, resigned because the armed forces were being too slow in building a border fence to keep out refugees and migrants.

Officials in Bavaria, the southern German state that has become the entry point for migrants arriving from Hungary via Austria, said about 4,400 had arrived in Munich on Monday. Another 1,500 were on trains heading on to cities elsewhere in Germany.

At Munich's international trade fair grounds, three halls have been given over to the effort, with more than 2,000 camp beds and a dining hall with hot food.

The few rucksacks and plastic bags the travelers had arrived with were scattered between the beds. Some children kicked a soccer ball around outside.

"For the families it's too hard. For the single guys I think it's good to come. If somebody has some money or a passport for a visa, it's better," said Hassan Halabi from Aleppo in Syria, who hopes to go to Konstanz on the Swiss border.

Merkel's welcome to migrants has been praised by human rights groups. But there were signs of dissent within her conservative camp, with officials from the Bavarian Christian Social Union (CSU), sister party of her Christian Democrats, criticising her handling of the crisis. There have also been attacks on shelters, including two early on Monday.

"There is no society that could cope with something like this," CSU leader and Bavarian premier Horst Seehofer said. "The federal government needs a plan here."