US whistleblower Edward Snowden has applied for asylum in Russia, hours after President Vladimir Putin said Moscow had no intention of handing him to the United States.

The New York Times on Monday quoted a Russian official as saying Snowden had applied for asylum in Russia, as well as 14 other countries that he did not name.

A Russian immigration official, who didn't want to be named, told Reuters news agency that a Wikileaks activist who is traveling with Snowden handed his application to a Russian consulate in the transit area at Moscow's Sheremetyevo airport late on Sunday.

It came hours after Putin said Moscow did not intend to hand him to US authorities, but said he must stop leaking information if he wished to remain in Russia.

Snowden "is not a Russian agent", Putin said on Monday, and that Russian intelligence services were not working with the fugitive American, who is believed to remain in the transit area at a Moscow airport eight days after arriving from Hong Kong.

"Russia never hands over anybody anywhere and has no intention to do so," he said.

However, "if he wants to remain here there is one condition - he should stop his work aimed at inflicting damage on our American partners no matter how strange this may sound coming from me."

Felony crimes

The State Department has declined to predict how the US would respond if Snowden was given asylum in Russia.

"Again, we're not at that point right now. We're going to continue to make our case about what we think needs to happen, and we hope they do the right thing," State Department spokesman Patrick Ventrell said.

The State Department spokesman said that Snowden was still a US citzen and had the right to a "fair" trial if he returned to his native country.

Ventrell rejected comments by WikiLeaks founder Julian Assange, who has described Snowden as being legally "marooned" in Moscow after Washington cancelled the leaker's US passport.

He told reporters that the US government could issue Snowden a "one entry travel document" to the United States as he is "accused of serious felony crimes".

Norms of international law

Al Jazeera's Peter Sharp, reporting from Moscow, said there hasn't been a spotting or report of Snowden in days and there was growing speculation he was perhaps not still in the transit area.

"When you look at the Russian media, who are very close to the FSB, some of the quotes coming from their unnamed sources, (Snowden has been called) a 'tasty morsel' as one put it.

"Here is an NSA contractor, what he has with him no one knows. He is rumoured to have laptops and disk drives with him, and (this) obviously would be a welcome addition to the FSB for questioning."

Putin said Snowden should choose his final destination and go there.

A senior Russian security official has said President Putin and US President Barack Obama had told FSB and the FBI, the security agencies of their respective countries, to seek a solution on the Snowden case, Russian RIA news agency reported.

Nikolai Patrushev, former head of the FSB and the current Secretary of the Security Council of Russia, made the statement during his appearance on Russia 24.

"Of course they do not have solutions that would suit both sides, that is why they have instructed the director of the FSB, Alexander Bortnikov and head of FBI, Robert Mueller, to be in constant contact and come up with options for solutions."

Patrushev added that "the task at hand is not a simple one, since [the FSB and the FBI] need to find a solution within the norms of international law".

"Today there is no ready to use formula" he said.