The crisis is intensifying due to a surge in migrantsfleeing war and poverty in Africa, Asia and the Middle East, and some European governments have refused to take in refugees and resisted EU proposals for a common plan to deal with the growing emergency.

The UN says the continuing conflict in Syria is a major factor behind the rise in migrant numbers.

State television channel M1 also reported thatmigrants with valid documents and train tickets were being allowed to board a train to Munich on Monday morning.

Since the checks began late on Sunday, more than 200 migrants have been picked up and five peoplearrested on suspicion of smuggling.

They are supposed to stay in Hungary until theirasylum requests are settled but many, along with many other migrants who have avoided being registered, quickly try to go to richer EU countries, especially Germany. As part of the clampdown, carried out in close collaboration with the Hungarian, Slovakian andGerman authorities, police are stopping trucks, vans and cars in an effort to catch those trying to make money from people fleeing war and persecution.

“If Europe fails on the question of refugees, then it won’t be the Europe we wished for”, she said on Monday.

Implicitly criticising countries like Slovakia that said they would reject migrants from majority Muslim countries, she said: “If we start saying “I do not want Muslims”… that cannot be good”.

Reuters reported Monday that migrants in Hungary are now being allowed onto trains bound for Vienna andGermany.

Austrian Railways had cited “overcrowding” on the train and a police spokesperson in Vienna said Austriawanted to check whether any of the migrants had already asked for asylum in Hungary.

The trains were halted near the Hungarian border town of Hegeshalom, where Austrian police proceeded to check their papers.

European Union ministers were summoned on Sunday to meet in two weeks’ time to seek urgent solutions to a migration crisis unprecedented in the bloc’s history, as the mounting death toll on land and sea forced governments to respond. “We can not accept it”.

France’s Prime Minister Manuel Valls agrees a fair distribution of asylum seekers in Europe is needed to prevent further deaths.

In France, European authorities have given five million euros (£3.6m) to build a new camp to help 1,500 migrants from Sudan, Eritrea and elsewhere gathered in Calais in an attempt to cross to Britain.

Hungary has been erecting a barbed wire fence along its more than 100-mile border with Serbia, which Fabius said should be taken down.

They were relieved to get to Macedonia after the end of violent clashes between migrants and police who tried to stop thousands of people streaming through to Serbia.

While critical of Hungary, Austrian authorities also acknowledged they were overwhelmed by the thousands who arrived by rail Monday evening.

A Palestinian-Syrian woman, travelling with her four-year-old daughter and other relatives, was unfazed.

Romania’s foreign ministry said on Sunday that 26 Romanians had been detained in Hungary recently, suspected of human trafficking.