He said Hungary would not allow migrants to leave its territory without registering.
Viktor Orban’s comments came as Hungarian authorities opened Budapest’s main rail station to hundreds of migrants after a two-day stand-off.
One train left, but then stopped near a migrant reception centre.
Migrants resisted efforts by police to get them off the train at Bicske, about 25 miles west of Budapest. Some were banging on the windows and shouting “Germany, Germany”.
EU rules place responsibility for assessing asylum claims on the country where a migrant first arrives.
Many of the migrants currently in Hungary have been refusing to register there, in order to continue their journeys to Germany before seeking asylum.
The migrants stuck at Budapest’s Keleti station were prevented from boarding trains on September 1 and 2. Some were involved in scuffles with police.
They had bought tickets after Hungary briefly appeared to abandon efforts to register migrants on August 31, allowing huge numbers to board trains to Vienna and southern Germany.
After the station opened on September 3, rail staff said international trains were indefinitely suspended, but international tickets would be accepted on internal trains.
The number of migrants entering Europe has reached record levels, with 107,500 arriving in July alone. Germany expects to take in 800,000 migrants this year – four times last year’s total.
The surge in numbers has created tension and disagreement over EU migration policy. Germany has been prepared to accept large numbers of asylum seekers, but other countries have not.
Viktor Orban, who heads the anti-immigrant Fidesz party and was in Brussels for talks, said border control was “the number one issue”.
During a tense press conference with European Parliament President Martin Schulz, PM Viktor Orban said that “nobody would like to stay in Hungary, neither in Slovakia nor Poland nor Estonia”.
“All of them would like to go to Germany,” he said.
“Our job is only to register them.”
Martin Schulz countered: “What we are seeing for the time being is egoism instead of common European sense.
“To say <<yeah, you know we have refugees all over in Europe but they all want to go to Germany and therefore we are not concerned>> is effective, but wrong. And therefore I think we need a fair and just distribution.”
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