Edward Snowden, the US whistleblower, is still in the transit zone of Moscow's Sheremetyevo airport, and is free to leave and should do so as soon as possible, Russian President Vladimir Putin has revealed.
During a visit to Finland on Tuesday, Putin said he hoped the affair would not affect Russia's relations with the US, which wants Russia to send the former National Security Agency (NSA) contractor to the US.
However, Putin hinted that Russia would not hand him over.
"We can only hand over foreign citizens to countries with which we have an appropriate international agreement on the extradition of criminals," he said, adding that Snowden has committed no crime in Russia.
Putin dismissed US accusations against Russia over the case as "rubbish", saying that Russian security agencies had not worked with Snowden.
Snowden has been charged by the US of espionage and spying after he revealed to Western newspapers how the NSA spies on the internet and phone activities of millions of people.
He has revealed details of two widespread surveillance programmes, one of them named PRISM, which is authorised by a secret court.
Earlier reports suggested that Snowden took a flight on Monday out of Moscow for Havana, apparently en route to Ecuador, having arrived in the Russian capital from Hong Kong the previous day.
Ricardo Patino, foreign minister of Ecuador, where Snowden is seeking asylum, said that the country knew nothing about his whereabouts or what documents he might be using to travel.
Ecuador, however, has said it is still considering Snowden's asylum request.
The US has annulled Snowden's passport and wants him returned to face espionage charges.
The US State Department says it has asked Russia to return Snowden, even in the absence of an extradition treaty between the two countries.
"It is accurate there is not an extradition treaty between Russia and the United States, but there are standards of behavior between sovereign nations," John Kerry, US secretary of state, said on Tuesday.
The amount of power Russia has was called in to question by journalists as Snowden has not officially entered Russia and remains in transit in the Moscow airport.
Russian law requires travellers who spend more than 24 hours in the airport's transit area to get a transit visa. It was unclear whether Snowden had sought or received a transit visa.
The US has also strongly criticised China for allowing Snowden to leave Hong Kong. In its response, China has said that the US accusations are "groundless and unacceptable".
Hua Chunying, a spokesperson for the Chinese foreign ministry, said that all parties should accept that the Hong Kong government had handled Snowden's case in accordance with the law.
The White House said Hong Kong's decision was "a deliberate choice by the government to release a fugitive despite a valid arrest warrant, and that decision unquestionably has a negative impact on the US-China relationship".
Meanwhile, Julian Assange, the founder of whistleblowing website Wikileaks, has described Snowden as "healthy and safe", but did not provide any details of his whereabouts.
Assange has been granted asylum by Ecuador in a separate case, and has been living in the country's London embassy for more than a year.
Against this backdrop, US Republican legislators criticised the Obama administration's handling of the Snowden case, calling Obama weak for failing to persuade Russia and China to return him to the US.
"It should cause a profound re-evaluation on our relationship with Russia and with Vladimir Putin, something that a lot of us have been saying for a long time," Senator John McCain said on Tuesday.
He described Putin as a "KGB colonel that has no interest in the same values and principles that we hold dear".