Snowden, who has been in hiding in Hong Kong for several weeks since he revealed information on the highly classified spy programs, has talked of seeking asylum in Iceland.
However, Russia's ITAR-Tass news agency cited an unidentified Aeroflot official as saying Snowden would fly from Moscow to Cuba on Monday and then on to Caracas, Venezuela.
The White House had no immediate comment about Snowden's departure, 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 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 anti-secrecy group WikiLeaks took credit for helping Snowden leave Hong Kong, saying on Twitter, "Mr. Snowden is currently over Russian airspace accompanied by WikiLeaks legal advisors."
Snowden's departure eliminates a possible fight between Washington and Beijing at a time when China is trying to deflect U.S. accusations that it carries out extensive surveillance of American government and commercial operations. 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.
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."
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."
Copyright 2013 The Associated Press.