Edward Snowden reportedly landed in Moscow on Sunday after Hong Kong let the former US intelligence technician leave its territory, despite Washington's efforts to extradite him to face espionage charges.
The anti-secrecy group WikiLeaks said Snowden was heading for a "democratic nation" which it did not name.
Ecuador's foreign minister, Ricardo Patino, wrote on Twitter on Sunday that Snowden had applied for asylum in his country. WikiLeaks editor-in-chief Julian Assange is currently living in Ecuador's embassy in London as he fights extradition to Sweden on sex assault charges.
The Ecuadorean ambassador in Moscow was also reported to be preparing to meet Snowden in the Russian capital.
"Snowden today voluntarily left Hong Kong for a third country through legal and normal means," a Hong Kong government spokesman said in a press statement earlier.
The statement added that Hong Kong had "not obtained adequate information" to handle a provisional arrest warrant for Snowden issued by the US. A government spokesman also said that Snowden, a former contractor with the National Security Agency (NSA), had left voluntarily.
Snowden flew out of Hong Kong on Sunday morning on board Aeroflot SU213 flight, a Chinese newspaper said.
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Al Jazeera's Craig Leeson, reporting from Hong Kong, said that other airlines heading to the UK were given memorandums earlier to look for Snowden if he boarded the plane.
Documents previously leaked by Snowden revealed that the NSA has access to vast amounts of Internet data such as emails, chat rooms and video from large companies, including Facebook and Google, under a government programme known as Prism.
Hong Kong, a former British colony, reverted to Chinese rule in 1997 and although it retains an independent legal system, and its own extradition laws, Beijing has control over Hong Kong's foreign affairs.
Russian president Vladimir Putin's spokesman, Dmitry Peskov, said earlier this month that Russia would consider granting Snowden asylum if he were to ask for it and pro-Kremlin lawmakers supported the idea, but there has been no indication he has done so.
Snowden's reported departure came despite a US arrest warrant and extradition request to authorities in Hong Kong, where he arrived on May 20.
The government statement said Hong Kong had written to the US "requesting clarification" of earlier reports about the hacking of computer systems in Hong Kong by US government agencies.
China's Xinhua news agency, referring to Snowden's accusations about the hacking of Chinese targets, said they were "clearly troubling signs".
It added: "They demonstrate that the United States, which has long been trying to play innocent as a victim of cyber attacks, has turned out to be the biggest villain in our age."