An 81-year-old former Marxist urban guerrilla who became a far-right extremist and was sentenced to 10 years in prison for Holocaust denial was arrested in Hungary on Monday after illegally leaving Germany, officials said.

The German news media reported that the extremist, Horst Mahler, had announced he was seeking asylum in Hungary, where the rightist government of Prime Minister Viktor Orban has repeatedly provoked the European Union with crackdowns on the press, political opponents, refugees, judges and academic institutions.

Ken Heidenreich, a spokesman for the prosecutor’s office in Munich, said in a telephone interview that his office had been informed that Mr. Mahler had been arrested in Hungary.

Hungarian officials initially said that they did not know about any arrest or asylum request, adding that if Mr. Mahler applied for asylum, he would be rejected, because he is a citizen of a European Union member country — namely, Germany.

On Monday afternoon, however, the police in Hungary announced that Mr. Mahler had been detained in Sopron, a city in the west of the country, near the border with Austria. Officials said it was likely he would be returned to Germany. ...