Meanwhile, authorities have struggled to enforce rules which ordinarily allow free movement within most of the EU but restrict travel by undocumented migrants.
Hundreds took to the tracks around France's Calais-Frethun station, the latest target for those trying to reach Britain, which many regard as a better place to live than countries on the continent.
Rail operator SNCF was forced to halt services near the entrance to the Channel Tunnel. Three Eurostar trains were blocked overnight and eventually continued to London early on Wednesday, while two returned to their departure stations.
Passengers on one London-bound train, which stopped less than a mile (1.6 km) from the tunnel, were told at one point to keep quiet and listen for people on the roof. A helicopter with a searchlight circled as guards walked the tracks.
With the power out, passengers sat in stifling darkness for nearly four hours. A woman in business class wept.
Eurostar later pulled the train back to Calais, where passengers disembarked for fresh air and bottled water.
About 3,000 to 4,000 migrants from the Middle East, Asia and Africa camp near Calais, dodging police as they try to board trains and trucks heading to Britain through the tunnel or on ferries. They have disrupted passenger and freight transport between Britain and France throughout the summer.
A spokeswoman for Eurotunnel, which operates the railway tunnel beneath the channel, said that as security has been tightened at Calais port and the tunnel entrance, migrants have targeted Calais-Frethun, about 5 km (three miles) inland, beyond a zone controlled by Eurotunnel.
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In Hungary, hundreds of migrants protested for a second day in front of Budapest's Keleti Railway Terminus, after they were blocked by police from boarding trains bound for Germany. The police said they must go to camps set up in Hungary instead.
Germany, which is prepared to take by far the greatest number of refugees, has begun accepting asylum claims from Syrians regardless of where they entered the EU, even though undocumented migrants are barred from travel across the bloc. That has caused confusion for neighboring countries, which have alternated between letting migrants through and halting them.
Italy announced new measures to add checks at its northern border in response to a German request.
Hungary is the main arrival point for those crossing the Balkans by land. A government spokesman said the country would observe EU rules which bar travel by those without valid documents.
"I want my freedom, I have been on the road for a very long time, and now I am in the European Union, and I want my freedom," said Sanil Khan, 32, leader of a group of about 100 young men who marched behind a cardboard cutout Afghan flag in a tight formation near a mainly peaceful crowd at the station.
The perils of the voyage were brought home by the images of a toddler in red t-shirt, blue shorts and tiny sneakers, washed up on the beach in Bodrum, Turkey. Turkish Police said at least 12 people had drowned from a group of 23 that had set off on two boats bound for a Greek island.
The migration crisis has confounded the EU, which is committed to the principle of accepting refugees fleeing real danger but has no mechanism to compel its 28 member states to share out the burden.
EU Commission President Jean-Claude Juncker is expected to unveil proposals in an annual state-of-the-union address to the European parliament next week.
Interior ministers hold an emergency meeting five days later.
The member states' envoys to Brussels held their first weekly meeting after a summer break and some diplomats detected a somewhat less divided atmosphere on the migrant issue - but sharp differences remain on how to share out responsibilities.
"The mood has changed," one said. "It was a little more consensual today.
There was a realization of the challenge Europe faces. There was more appetite to do more."
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Opinion across Europe has been increasingly polarized: German soccer fans have unveiled "refugees welcome" banners at matches, while a popular British newspaper columnist called migrants "cockroaches".
Countries like Italy, Greece and Hungary, where most migrants arrive before heading for richer countries further north, say they need more help from EU partners.
Greece, where around 2,000 people have been arriving per day on beaches in dinghies, announced plans for a new operations center and said it would improve conditions at camps the United Nations has described as "shameful". Four Bulgarians and two Turkish citizens had been arrested for trafficking 103 migrants in trucks, it said.
Germany has been the most welcoming, with plans to accept hundreds of thousands of refugees this year alone, adding 3.3 billion euros ($3.7 billion) to its welfare bill next year. A record 104,460 asylum seekers arrived in Germany last month, and more than 400,000 migrants have registered in a German computer system since the start of the year.
But that has caused chaos for neighbors and threatened the Schengen system that abolished frontier checks among 26 European countries. Berlin says that despite its decision to accept asylum applications from Syrians who arrive elsewhere in the EU, other EU states must still demand migrants remain in the countries where they first register.
At the opposite end of the spectrum of openness is Britain, which so far has accepted just 216 Syrian refugees under a scheme in partnership with the United Nations, as well as around 5,000 that managed to reach Britain and apply on their own.
"We have taken a number of genuine asylum seekers from Syrian refugee camps, and we keep that under review, but we think the most important thing is to try to bring peace and stability to that part of the world," Prime Minister David Cameron said. "I don't think there is an answer that can be achieved simply by taking more and more refugees."