ZURICH (Reuters) - The tide of migrants coming to Europe from the Middle East and Africa may be part of a left-wing plot to pack the continent with sympathetic voters, Hungarian Prime Minister Viktor Orban has told a Swiss magazine.

Orban's anti-immigrant rhetoric and the border fences he has erected to block the wave of people fleeing war and poverty have made him a winner at home from a crisis that has divided Europe.

"I am not brave enough to speak about this in public with certainty, but you cannot get around imagining that some kind of master plan is behind this," he said in an interview with Die Weltwoche published on Thursday.

He cited essays by "the European left and radical American democrats" that envision the emergence of a European super state to the detriment of traditional nation-states.

"Migration is seen as an opportunity ... All indications and experience suggest that the overwhelming majority of these migrants will vote for the left once they become citizens, so future leftist voters are being imported to Europe," he said.

Asked why conservatives such as German Chancellor Angela Merkel had offered a welcome to migrants, he said: "Many of us are racking our brains about this. Germany is the key. If the Germans tomorrow morning said 'We are full, that's it', the flood would stop immediately."

He said he suspected Merkel's hands were tied by her coalition with the center-left Social Democrats.

European Union countries are deeply split over how to respond to the sudden and massive influx.

Slovenia began erecting a razor wire fence along parts of its border with Croatia on Wednesday, saying it wanted better control over the migrants flowing through en route to northern Europe.

Orban has said Hungary does not want Muslims in large numbers, and that migrants are coming to Europe not to flee danger but rather because they want "a German or perhaps a Swedish life".

Austrian Chancellor Werner Faymann has likened Orban's policies to those of the Nazis, an allegation Hungary has rejected. The U.S. ambassador to Budapest has warned against "xenophobic characterization of refugees".

(Reporting by Michael Shields; Editing by Kevin Liffey)