The Federal Migration Service confirmed he had completed the relevant paperwork at Moscow's Sheremetyevo airport, where he has been for the past three weeks.
Mr Snowden is wanted by the US for leaking details of government surveillance programmes.
He has no travel documents, so has been unable to take up asylum offers from a number of Latin American states.
"He reached the conclusion that he needs to write an application for temporary asylum, and this procedure has just been done," said Anatoly Kucherena, a lawyer with strong links with the Kremlin who helped Mr Snowden with the paperwork.
"For now he is not going to go anywhere. For now he plans to stay in Russia," he said.
Meanwhile the White House reiterated its position that the fugitive should be expelled and face trial in the US.
By Daniel SandfordBBC News, Moscow
If there is a chance to grant Edward Snowden temporary asylum and then move him on to Latin America before September, that may be the best route for Russia.
But if that proves impossible, President Vladimir Putin will have to make a decision - does he continue to rub salt into America's wounds, or does he encourage Edward Snowden to leave quickly by making it clear that the asylum request is not going to work out.
What is still unclear is the extent to which the Russian intelligence agencies have been able to pump Edward Snowden for information, or even for the secret files themselves.
If they still want the information, there may be a trade-off involved - he gives the Russians what they desire and gets to leave the airport, and they decide that a poorer relationship with the US is the price they will have to pay for Mr Snowden's secrets.
"Mr Snowden should not be allowed to engage in further international travel except as necessary to return to the United States," spokesman Jay Carney said.
"He is not a human rights activist. He is not a dissident. He's accused of leaking classified information."
Mr Kucherena said the fugitive had stated in the application that he faced possible torture and execution if he returned  to the US.
If his application is accepted, he will be free to work and move freely in Russia, said the lawyer.
Russia's Interfax news agency quoted Mr Kucherena as saying he had asked Mr Snowden whether he would observe a request from President Vladimir Putin to not harm US interests if he is able to leave the airport.
"He replied: 'I will observe this condition'," Mr Kucherena told the agency.
Officials said Mr Snowden might be moved to an airport facility for accommodating refugees while his application was being processed, which should take no more than three months.
A presidential spokesman told Interfax that Mr Putin had not yet responded to the asylum request, and that the decision on whether it would be granted was not his to make.
But although the Russian government insists the decision will be made by a relatively junior official, the person in charge will be in no doubt what his boss would like him to do, says the BBC's Daniel Sandford in Moscow.
Who is Edward Snowden?
Where will Snowden end up?
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President Putin is clearly aware of the sensitivities involved, and the issue risks overshadowing talks with US President Barack Obama who is due to visit Russia in September, our correspondent adds.
Mr Snowden arrived in Russia on 23 June, having left Hong Kong, from where he had issued his leaks to the media.
He held a news conference at the airport on 12 July, where he said he was seeking asylum in Russia.
He has sent requests for political asylum to at least 21 countries, most of which have turned down his request. However, Bolivia, Nicaragua and Venezuela have indicated they could take him in.
But he is unable to leave the transit zone as he currently has no asylum documents or Russian visa, and the US has revoked his passport.
Some European countries are likely to close their airspace to any plane suspected of carrying the fugitive.
Meanwhile on Tuesday groups from across the political spectrum, including gun rights groups, churches and human rights groups filed a lawsuit demanding that the US National Security Agency hand over and destroy all the telephone communication data it has.
The lawsuit alleges the collection of phone records is an "illegal and unconstitutional programme of dragnet electronic surveillance". The US justice department has not commented on the case.
Mr Snowden's leaking of thousands of classified US intelligence documents has led to revelations that the National Security Agency is systematically seizing vast amounts of phone and web data.
The documents have also indicated that both the UK and French intelligence agencies allegedly run similarly vast data collection operations, and the US has been eavesdropping on official EU communications.

Sum: Fugitive US intelligence leaker Edward Snowden has applied for temporary asylum in Russia, officials say.


The UNESCO World Heritage Site was the overall winner of the England's Great Places awards.
The competition was run by the Royal Town Planning Institute (RTPI), to show off the most "attractive and inspiring" work of town planners.
Thame High Street in Thame, Oxfordshire, and Saltaire near Bradford came second and third respectively.
The city of Bath and the Peak District were also named among the top 10 finalists.
Liverpool waterfront, which features the landmark buildings known as Three Graces, topped the list after more than 11,000 people voted.
Janet Askew, president of the RTPI, said:  "I think Liverpool is a great place and I think there is loads coming on in Liverpool now.
"There has been so much happening recently linking Liverpool One with the waterfront itself and to the spectacular buildings of the Cunard and the Liver and the designation of the World Heritage site."
She added: "All these things come from good planning I think perhaps the public has just suddenly woken up to it."
Liverpool mayor Joe Anderson said the waterfront was "recognised around the world" as a "unique" area, combining business and tourism.
Liverpool waterfront
The area stretches along the waterfront from Albert Dock, through The Pier Head and up to Stanley Dock, and up through the historic commercial districts and the RopeWalks area to St George's Quarter
It was granted World Heritage Site status by UNESCO in 2004, reflecting the city's significance as a commercial port
The Pier Head encompasses a trio of landmarks known as the Three Graces - the Royal Liver Building, the Cunard Building and Port of Liverpool Building
The Albert Dock, designed by Jesse Hartley, opened in 1846 and remained a fully working dock until closing in 1972. It later underwent a restoration programme and was reopened as a visitor attraction in 1988.
Source: Visit Liverpool/UNESCO

Sum: Liverpool's waterfront has won a national competition to find the "greatest places" in England.


His appointment was ratified earlier after he was chosen by new Police and Crime Commissioner Sue Mountstevens.
Mr Gargan, the former chief constable and chief executive of the National Policing Improvement Agency (NPIA), is due to start work on 1 March.
He replaces Colin Port who is retiring at the end of the month after refusing to re-apply for his own job.
Mr Gargan's appointment was officially confirmed by a meeting of the force's police and crime panel following his selection last week.
The selection process was threatened when the current chief constable, Mr Port, mounted a legal challenge to the decision by the commissioner to open up his job for interview when his existing contract runs out on 26 January.
Mr Port's application for an injunction to stop the selection process for his successor was refused by a high court judge.
Mr Gargan, who is also a previous assistant chief constable of the Thames Valley force, said it had been a "turbulent time" but he hoped to repay the confidence of the PCC and the panel through "hard work and common sense".
He said: "I acknowledge the contribution of Colin Port - we go back a long way and I have nothing but respect for him and his achievements.
"But I do understand that as the new chief, people will be looking at me to settle things down and basically just get on with the job."

Sum:
Nick Gargan has been officially confirmed as the new Chief Constable of Avon and Somerset Police.