According to ABC News, Snowden's U.S. passport was revoked on Saturday. An Aeroflot flight from Hong Kong carrying Snowden landed in Moscow Sunday morning.
Hong Kong authorities were notified of Snowden's annulled passport, but an official told ABC News that the U.S. notification may have occurred after Snowden already departed the city.
WikiLeaks, which says it is giving Snowden legal assistance, said in a statement that the former National Security Agency contractor's asylum request will be formally processed once he arrives in Ecuador. Ricardo Patino, the country's foreign minister, said on his Twitter account that his government had received a request for asylum from Snowden Sunday.
"We are analyzing it with a lot of responsibility," Foreign Minister Ricardo Patino told reporters Monday through a translator at a hotel in Hanoi, Vietnam.
He says the decision "has to do with freedom of expression and with the security of citizens around the world."
Patino spoke briefly to reporters on his way to a meeting with Vietnam's foreign minister. He did not say how long it would take Ecuador to decide.
An Aeroflot flight from Hong Kong believed to be carrying Snowden landed in Moscow Sunday morning.
Hong Kong's government allowed Snowden to leave. Russia's ITAR-Tass news agency cited an Aeroflot airline official as saying Snowden intended to fly to Cuba Monday then on to Caracas, Venezuela.
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.
Snowden had been in hiding in Hong Kong for several weeks since he revealed information on highly classified U.S. surveillance programs.
The White House had no immediate comment about the departure, which came a day after the U.S. made a formal extradition request and warned 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."
Russian officials have given no indication that they have any interest in detaining Snowden or any grounds to do so. Foreign Minister Sergey Lavrov has said that Russia would be willing to consider granting asylum if Snowden were to make such a request.
Russia and the U.S. have no extradition treaty that would oblige Russia to hand over a U.S. citizen at Washington's request.
The Cuban government had no comment on Snowden's movements or reports he might use Havana as a transit point.
Snowden's departure comes as Chinese media released new allegations from Snowden that U.S. hacking targets in China included the nation's cellphone companies and two universities.
The Associated Press contributed to this report.