Russia has demanded that Georgia explain why it allowed Russian tycoon Boris Berezovsky to visit the Caucasus republic without arresting him.
Boris Berezovsky: Flew in under false name on private plane
The billionaire, who has been granted political asylum in Britain, flew into Tbilisi by private jet on Tuesday night - to visit a friend, he said.
The Russian foreign ministry said Georgia should have acted on an international warrant for his arrest.
Mr Berezovsky is wanted in Russia on fraud and embezzlement charges.
The Georgian ambassador to Moscow was summoned to the foreign ministry and was told that Russia "demands explanations why Georgian law enforcement agencies failed to take appropriate measures to detain Berezovsky and hand him over".
The visit came at a sensitive time for Georgia, in the wake of former President Eduard Shevardnadze's resignation amid mass protests.
In a further sign of instability, a powerful explosion rocked the state television centre in Tbilisi on Wednesday.
The blast interrupted the evening news programme and shattered windows. No one was injured.
Earlier, a top Georgian border control official, Valery Chkheidze, reported that four people arrived in Tbilisi on a private jet from London - two Russians, a French citizen and "one British, by the name of Elein Platon, whose photograph and appearance suggest that it was Boris Berezovsky".
Mr Berezovsky later confirmed the visit on Ekho Moskvy radio.
"I don't think there was any risk since I received political asylum from Britain and there are countries that recognise political asylum," he said.
He said he used an assumed name because "the British Government... is protecting me from pursuit by Russian authorities" by issuing him "documents with different surnames."
Georgian Interior Minister Georgy Baramidze told the AFP news agency that "Berezovsky... is a free person, he has a right to fly into Georgia".
Mr Berezovsky, who was among a group of "oligarchs" closely associated with former Russian President Boris Yeltsin, left Russia three years ago after falling out with his successor Vladimir Putin.
He has since become a fierce critic of the regime, and claims the fraud case against him is political.
In February 2002, Mr Berezovsky admitted giving money to Chechen separatists, who are engaged in a bitter war against Russian forces. But he insisted that the donation was intended for a cement factory.