MOSCOW (Reuters) - Russia angrily denied U.S. media reports that the Russian director of a cultural exchange programme may be recruiting Americans as spies, saying such allegations risked damaging ties between the two countries.

Media outlets including Mother Jones magazine said the Federal Bureau of Investigation was interviewing Americans who participated in an exchange programme directed by Yuri Zaitsev, who heads the Russian Centre for Science and Culture in Washington.

Law enforcement officials said the FBI was investigating whether Zaitsev and Rossotrudnichestvo, the government agency responsible for the programme, had used trips to Russia to recruit Americans, the Washington Post reported.

It cited one official as saying Zaitsev created files on some participants - who in some cases stayed in luxury hotels and met state officials on visits to Russia - allegedly to cultivate them as future intelligence assets.

In a statement on Thursday, Russia's Foreign Ministry said it was "bewildered" by the reports.

"The fabrications they contain bear no relation to reality," it said.

The ministry said Rossotrudnichestvo has been organising short visits to Russia for young politicians, scientists, business people and others since 2011 and that more than 1,000 people from 50 countries had visited.

It said the programme was in line with calls by leaders of both countries for cultural exchanges.

"We believe the publications and the actions by the American authorities are unfriendly," the ministry said.

"It is necessary for the U.S. authorities to unequivocally and publicly distance themselves from ill-intentioned attempts to cast a shadow over activity of the Russian Centre for Science and Culture in Washington," it said.

Ties between Russia and the United States have been strained by disputes over human rights, espionage, the Syria conflict and other issues including the Kremlin's treatment of critics since President Vladimir Putin returned to the Kremlin last year.

(Writing by Steve Gutterman; editing by Tom Pfeiffer)