* Russia says journalist violated visa regulations
* Satter says ministry statement is false
* Move echoes Cold War, precedes Winter Olympics (Adds additional comments from Satter)
By Timothy Heritage and Gabriela Baczynska
MOSCOW, Jan 14 (Reuters) - Russia has barred a U.S. journalist critical of President Vladimir Putin from the country for five years, in a move that could upset relations with the United States and has echoes of the Cold War.
Moscow's treatment of David Satter could fuel concern about freedom of speech before the Winter Olympics in Sochi next month, although Putin has tried to appease critics by freeing former oil tycoon Mikhail Khodorkovsky and members of the Pussy Riot protest group in the run-up to the Games.
"I was expelled from the country," Satter wrote on his personal website. "This is an ominous precedent for all journalists and for freedom of speech in Russia."
The Foreign Ministry said on Tuesday that Satter, author of three books on Russia and the Soviet Union, had been prevented from returning to Russia last month after grossly violating visa regulations.
In a website entry, he dismissed the official version of events, saying he had followed all instructions, and he blamed the foreign ministry, which handles foreign journalists' media accreditation, for causing delays that led to his expulsion.
Satter said that he had flown to Kiev to receive a new letter of invitation but instead received only a statement read to him by a Russian diplomat there declaring him persona non grata.
"The competent organs have decided that your presence on the territory of the Russian Federation is undesirable. Your application for entry into Russia is denied," the statement said.
Such expulsions have been rare since the end of the Cold War and collapse of the communist Soviet Union in 1991. But the ministry dismissed suggestions by Western media that the move against Satter was politically motivated as "tendentious".
A former Moscow correspondent for the Financial Times, Satter was back in the Russian capital last year and advising Radio Free Europe/Radio Liberty, a broadcaster funded by the U.S. government.
BOOK ON BOMBINGS
In one of his books, "Darkness at Dawn", Satter accused the Federal Security Service (FSB), a successor of the Soviet-era KGB, of being responsible for bombings of Russian apartment buildings in 1999 which killed more than 300 people.
The FSB, which was headed by Putin before he became prime minister and then president, has denied the charge. Russian authorities blamed the attacks on separatists from Chechnya in the volatile North Caucasus. The crimes were never solved.
The Foreign Ministry in a statement said Satter had failed to report to the federal migration service as required when he last arrived in Russia on Nov. 21.
"In fact, from Nov. 22 to Nov. 26 this U.S. citizen stayed on Russian territory illegally," the ministry said, and a Moscow court had ruled on Nov. 29 that he should be expelled. A court spokeswoman confirmed the ruling.
Satter said the ministry had delayed giving him an invitation, causing him to go to court and pay a fine before flying to Kiev to start the visa process again.
The ministry said Satter had left Russia on Dec. 4 and was refused a visa when he wanted to return. He was just one of about 500,000 foreigners barred from Russia for periods of three to 10 years for breaking the law, the ministry added.
Radio Free Europe/Radio Liberty said the U.S. embassy in Moscow had sought an explanation from the Russian authorities, without success.
Relations between Moscow and Washington improved during U.S. President Barack Obama's first-term push to "reset" ties.
But they have deteriorated again amid disputes on Iran, Syria, human rights and Russia's decision to give temporary asylum to American fugitive spy contractor Edward Snowden.
Russia expelled a U.S. diplomat in Moscow last year, accusing him of working as a spy and trying to recruit a Russian agent for the Central Intelligence Agency (CIA).
Public announcements of such expulsions have become rare since the end of the Cold War.
Satter is currently in London. (Additional reporting by Thomas Grove and Vladimir Soldatkin; editing by Andrew Roche)