"The problem is not a European problem, the problem is a German problem," Orban told a press conference with European Parliament President Martin Schulz in Brussels.
"Nobody wants to stay in Hungary, neither in Slovakia, nor Poland, nor Estonia. All want to go to Germany. Our job is just to register them."
Orban's comments came as hundreds of refugees and migrants stormed a train at Budapest's reopened main international railway station, which has become a flashpoint for people trying to head to western Europe via Hungary.
"We have clear cut regulations at the European level. German Chancellor (Angela Merkel) ... said yesterday that nobody could leave Hungary without being registered," he added.
"If the German chancellor insists that we register them, we will, it is a must."
Orban has taken a consistently hard line on the migrant crisis engulfing Europe, refusing to accept an EU plan for compulsory quotas for asylum seekers and building a razor wire fence along the border with Serbia in a bid to halt the influx.
The fence has done little to stem the flow and Hungary remains a key arrival point for tens of thousands of migrants entering the European Union, with some 50,000 arriving in the country in August alone.
Orban was due to hold talks with European Commission chief Jean-Claude Juncker and with EU president Donald Tusk, who warned earlier Thursday that divisions between EU member states threatened to scupper efforts to find a common response.
Schulz also warned that the 28 member states had to act as one.
"The European idea is of solidarity; what we see at the moment is egoism and to my mind, this is a real threat to the EU," he said.