Snowden was believed to have landed in Russia on Sunday after being allowed to leave Hong Kong.
He was on an Aeroflot flight from Hong Kong that arrived in Moscow shortly after 5 p.m. (1300gmt) Sunday and was booked on a flight to fly to Cuba on Monday, the Russian news agencies ITAR-Tass and Interfax reported, citing unnamed airline officials.
Snowden did not leave Moscow's Sheremetyevo Airport with the other passengers and was not seen by a crowd of journalists waiting in the arrivals lounge. Interfax reported that he was spending the night in the transit zone of the airport because he did not have a visa to enter Russia and had rented a room in a capsule hotel.
The White House had no immediate comment about the departure from Hong Kong, which came a day after the United States made a formal request for his extradition and gave a pointed warning to Hong Kong against delaying the process of returning him to face trial in the U.S.
The Department of Justice said only that it would "continue to discuss this matter with Hong Kong and pursue relevant law enforcement cooperation with other countries where Mr. Snowden may be attempting to travel."
The Hong Kong government said in a statement that Snowden left "on his own accord for a third country through a lawful and normal channel."
It acknowledged the U.S. extradition request, but said U.S. documentation did not "fully comply with the legal requirements under Hong Kong law." It said additional information was requested from Washington, but since the Hong Kong government "has yet to have sufficient information to process the request for provisional warrant of arrest, there is no legal basis to restrict Mr. Snowden from leaving Hong Kong."
The statement said Hong Kong had informed the U.S. of Snowden's departure. It added that it wanted more information about alleged hacking of computer systems in Hong Kong by U.S. government agencies which Snowden had revealed.
The signal that Hong Kong had let Snowden go on a technicality appears to be a pragmatic decision aimed at avoiding a drawn out extradition battle. The move swiftly eliminates a geopolitical headache that could have left it facing pressure from both Washington and Beijing.
Hong Kong, a former British colony, has a high degree of autonomy and is granted rights and freedoms not seen on mainland China, but under the city's mini constitution Beijing is allowed to intervene in matters involving defense and diplomatic affairs.
Hong Kong has an extradition treaty with the U.S., but the document has some exceptions, including for crimes deemed political.
Russian officials have given no indication that they have any interest in detaining Snowden or any grounds to do so. Russia and the United States have no extradition treaty that would oblige Russia to hand over a U.S. citizen at Washington's request.
WikiLeaks said it was providing legal help to Snowden at his request and that he was being escorted by diplomats and legal advisors from the group. Its founder, Julian Assange, who has spent a year inside the Ecuadorean Embassy in London to avoid extradition to Sweden to face questioning about sex crime allegations, told the Sydney Morning Herald that his organization is in a position to help because it has expertise in international asylum and extradition law.
The Cuban government had no comment on Snowden's movements or reports he might use Havana as a transit point.
The Obama administration on Saturday warned Hong Kong against delaying Snowden's extradition, with White House national security adviser Tom Donilon saying in an interview with CBS News, "Hong Kong has been a historically good partner of the United States in law enforcement matters, and we expect them to comply with the treaty in this case."
Michael Ratner, Assange's lawyer, said he didn't know Snowden's final destination, but said his options were not numerous.
"You have to have a country that's going to stand up to the United States," Ratner said. "You're not talking about a huge range of countries here."
Ratner said a country's extradition treaty with the U.S. is "not going to be relevant" because the country he ends up going to will likely be one willing to give him a political exemption.
Snowden's departure came as the South China Morning Post released new allegations from Snowden that U.S. hacking targets in China included the nation's cellphone companies and two universities hosting extensive Internet traffic hubs.
He told the newspaper that "the NSA does all kinds of things like hack Chinese cellphone companies to steal all of your SMS data." It added that Snowden said he had documents to support the hacking allegations, but the report did not identify the documents. It said he spoke to the newspaper in a June 12 interview.
With a population of more than 1.3 billion, China has massive cellphone companies. China Mobile is the world's largest mobile network carrier with 735 million subscribers, followed by China Unicom with 258 million users and China Telecom with 172 million users.
Snowden said Tsinghua University in Beijing and Chinese University in Hong Kong, home of some of the country's major Internet traffic hubs, were targets of extensive hacking by U.S. spies this year. He said the NSA was focusing on so-called "network backbones" in China, through which enormous amounts of Internet data passes.
The Chinese government has not commented on the extradition request and Snowden's departure, but its state-run media have used Snowden's allegations to poke back at Washington after the U.S. had spent the past several months pressuring China on its international spying operations.
A commentary published Sunday by the official Xinhua News Agency said Snowden's disclosures of U.S. spying activities in China have "put Washington in a really awkward situation."
"Washington should come clean about its record first. It owes ... an explanation to China and other countries it has allegedly spied on," it said. "It has to share with the world the range, extent and intent of its clandestine hacking programs."
Chan reported from Hong Kong. Sylvia Hui in London, Paul Haven in Havana, and Anne Flaherty and Julie Pace in Washington contributed to this report.