Russian President Vladimir Putin has told fugitive former CIA-analyst Edward Snowden to stop leaking US secrets if he wants to remain in the country.
He said Moscow had never extradited anyone before and "has no intention to do so", adding Mr Snowden was free to go if granted asylum elsewhere.
Edward Snowden, 30, is believed to be holed up in a Moscow airport hotel.
The US wants to prosecute him over the leaking of thousands of classified intelligence documents.
The leaks have led to revelations that the US is systematically seizing vast amounts of phone and web data.
At the weekend, Germany's Der Spiegel newspaper and Britain's The Guardian newspaper publicised allegations that the US has been spying on its EU allies.
The revelations have angered many EU countries which are demanding a response from Washington.
French President Francois Hollande has warned that negotiations over a major EU-US trade deal planned for next week could be threatened unless Washington can guarantee the spying stops "immediately".
'High level' talks
"Russia never hands over anybody anywhere and has no intention to do so," Mr Putin told a news conference in Moscow.
"If he (Snowden) 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."
This is the clearest indication yet, says the BBC's Steve Rosenberg in Moscow, that Mr Putin is keen to avoid damaging relations with Washington over the Snowden case.
The Russian president also stressed Mr Snowden "is not our agent and does not co-operate with us", and Russian secret services "never worked with him and are not working with him now".
Earlier, senior Russian official Nikolai Patrushev said both President Putin and his US counterpart, Barack Obama, had told the chiefs of their security services to seek a resolution to the stand-off over Mr Snowden.
Mr Patrushev, secretary of Russia's Security Council, told Russian media that the FSB and the FBI had been told to "keep in contact and find solutions", but warned there was no simple solution to the situation. The FBI refused to comment.
Mr Putin was speaking at the same time President Obama confirmed to reporters that Washington had held "high level" discussions with Russia about Mr Snowden.
"We don't have an extradition treaty with Russia," he told reporters while on a visit to Tanzania.
"On the other hand, Mr Snowden, we understand, has travelled there without a valid passport and legal papers. And we are hopeful the Russian government makes decisions based on the normal procedures regarding international travel and the normal interactions law enforcement have."