Writing in a German magazine he said his country had been "over run" by refugees arriving from the Middle East and Africa.
He urged European governments to get control of their borders before deciding how many asylum seekers they were going to take.
The majority of the people arriving in need of help were Muslim, Mr Orban said.
He added: "That is an important question, because Europe and European culture have Christian roots. Or is it not already and in itself alarming that Europe's Christian culture is barely in a position to uphold Europe's own Christian values?
"The people want us to master the situation and protect our borders. Only when we have protected our borders can questions be asked about the numbers of people we can take in, or whether there should be quotas."
Many of the people are trying to reach Germany through Hungary, prompting Mr Orban to say the refugee crisis was a "German problem".
Meanwhile migrants have poured into Budapest's Keleti railway station after police stopped blocking its main entrance, and hundreds piled into trains despite announcements that there were no services to western Europe.
Hungary's railway company said it had suspended all direct trains from the Hungarian capital to western destinations "in the interests of railway transport security".
Crowds of migrants dashed into the station as police withdrew, and boarded trains waiting at the platforms despite announcements, including in English over station loudspeakers, that the trains were not heading west.
Some migrants could be seen getting off the domestic trains, while others remained on the carriages amid the confusion.
Hungary, which for months permitted most applicants to head west after short bureaucratic delays, now says it will not let more groups deeper into the European Union and claims EU backing for the move.
