By Marton Dunai

BUDAPEST (Reuters) - Hundreds of migrants protested in front of Budapest's Keleti Railway Terminus for a second straight day on Wednesday, shouting "Freedom, freedom!" and demanding to be let onto trains bound for Germany from a station that has been closed to them.

Chaos this week at the station in the Hungarian capital has become the latest symbol of Europe's migration crisis, the continent's worst since the Balkan wars of the 1990s.

More than 2,000 migrants, including families with children, were waiting in the square at the station while Hungarians with IDs and foreigners with valid passports could board the trains.

About 300 migrants stared down police in riot gear on one side of the station. One waved a makeshift sign saying 'We Want Our Freedom'.

Hundreds of thousands of refugees fleeing war and economic migrants escaping poverty have been arriving in Europe, on rickety boats across the Mediterranean and over land across the Balkan peninsula.

Nearly all reach the EU on its southern or eastern outskirts and then press on for the richer and more generous countries further north and west, ignoring EU rules which require them to wait for processing in the country where they first arrive.

Germany, which is prepared to take by far the greatest number, has begun accepting asylum claims from Syrian refugees regardless of where they entered the EU, even though undocumented migrants are theoretically barred from travel across the bloc. That has caused confusion for its neighbors, which have alternated this week between letting them through and blocking them.

Many have come overland across the Balkans through Hungary, which allowed thousands to board trains for Germany on Monday but has since called a halt to the travel, leaving migrants camped in the summer heat in central Budapest.

ENFORCING RULES

Asked if Hungary would again let migrants board trains to Germany as it did on Monday, a government spokesman said that Budapest would observe European Union rules which bar travel by those without valid documents. The station has been shut to migrants since Tuesday morning.

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"A train ticket does not overwrite EU rules," spokesman Zoltan Kovacs added.

Hungary's parliament on Thursday begins an extraordinary session and is expected to vote on government proposals that tighten border controls, allowing for the use of the army in limited ways, and set up new holding camps for migrants.

The aid group Migration Aid, which has handed out food, water, blankets, and information to migrants for most of the summer, said the government's plans amounted to fear mongering.

"The rhetoric of the Hungarian government has demonized certain groups of people in order to generate fear and thus justify security measures, such as the potential intervention of the army at the Hungarian-Serbian border," it said in a statement.

Migration Aid will march from the Western railway terminus to the country's Parliament on Wednesday evening to protest against the planned legal changes but said it would also encourage the migrants to complete the registration process.

"Right now they refuse to go to camps and want to travel onwards, which creates a dangerous amount of tension. With a completed registration process and a card that proves it they can at least go anywhere inside Hungary," Migration Aid leader Zsuzsanna Zsohar told Reuters.

CONFOUNDED

The migration crisis has polarized and 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 of receiving them.

Twenty-six European countries have eliminated border controls between them under the EU's Schengen program, leaving no effective mechanism in place to enforce the ban on undocumented migrants traveling within the bloc.

Germany says that despite its decision to accept asylum applications from Syrians who first arrive elsewhere in the EU, other states in the bloc should continue to demand migrants register and remain where they first arrive.

With about 50 police blocking the main gates to the Budapest train station, migrants filled the large sunlit square in the morning, playing cards, sleeping or charging their phones on electrical outlets shared by television satellite trucks.

Willi Xylander, a 59 year-old German on holiday in Budapest, checked out the scene, wondering if it was safe for passage for regular travelers, including his wife and daughter who would be arriving the next day.

"We have heard so many stories about protests here that we were concerned," he said.

Agnes Halmos, a 30 year-old nurse, said she was more sorry for the migrants than scared of them.

"It's horrible that they are stuck here, thousands of them with just five portable toilets and no place to spend a night," she said. "There are infants here, for crying out loud!"

The relative calm was abruptly interrupted as a group of about 100 young men approached the square, marching behind a cardboard cutout Afghan flag in a tight formation.

Their leader, 32-year-old Sanil Khan, said they had spent long enough in Budapest and now they want to move on to Germany.

"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," he said, visibly agitated.

As the column of men arrived in front of the train station, they were immediately joined by hundreds of others, who broke into loud cheers and chants of "Freedom, freedom!" and "Germany, Germany!"

A young Middle Eastern man in his twenties, wearing a reversed baseball cap and a windbreaker emblazoned with the logo "CIA", was lifted above the crowd. He called out to the crowd: "Where do you want to go?"

"Germany!" they shouted back.

Hungarian police said in a statement they were acting in compliance with the Schengen code of border controls. They had stopped a van on the motorway leading from the Serbian border to Budapest which carried 10 Syrian and 10 Iraqi migrants and detained the Serbian driver on suspicion of human trafficking.

(Writing by Krisztina Than and Marton Dunai; Editing by Peter Graff and Anna Willard)