UPDATE 2-Snowden stays out of sight after leaving Hong Kong
* Snowden keeps low profile, seeks asylum in Ecuador
* Ecuador envoy visits airport hotel
(Adds speculation on Snowden whereabouts, quotes)
MOSCOW, June 23 (Reuters) - Former U.S. spy agency contractor Edward Snowden kept people guessing about his whereabouts and plans on Sunday after fleeing Hong Kong for Moscow.
Snowden, who is wanted by Washington after leaking details about U.S. surveillance, stayed out of sight after the plane he was believed to be on landed at Moscow's Sheremetyevo airport.
A source at the Russian airline Aeroflot said Snowden would fly to Cuba on Monday and was expected to go on to Venezuela, although Ecuador later said he had asked it for asylum.
Passengers arriving from Hong Kong said he may have been whisked away from the runway by waiting cars, initially prompting speculation he may spend the night in a foreign embassy in the Russian capital.
"There were a lot of police and black cars when we were getting off the plane," said a passenger who gave his name only as Olivier.
But a source at an airport hotel said he had spotted Snowden there and Ecuador's ambassador to Russia, Patricio Alberto Chavez Zavala, later spent several minutes inside the building.
The envoy told reporters as he went in that he expected to have talks with Snowden and Sarah Harrison, a representative of the WikiLeaks anti-secrecy group.
"We're waiting for Sarah. We're going to talk to them," the envoy said at the Capsule Hotel, which is intended for transit passengers who do not have a visa to enter Russia.
Ecuador later confirmed it had received an asylum request from Snowden but the ambassador declined to give more details and did not make clear if Snowden was inside the hotel.
POSSIBLE ASLYUM IN RUSSIA?
There was speculation in Moscow earlier on Sunday that Snowden might seek to stay in Russia, whose leaders accuse the United States of double standards on democracy and have championed public figures who challenge Western governments.
But Putin's spokesman, Dmitry Peskov, said he was unaware of Snowden's plans and the Foreign Ministry declined immediate comment on whether he had asked for asylum.
Alexei Pushkov, head of the lower house of parliament's foreign affairs committee, said it was not clear whether Moscow might offer Snowden asylum - a move that could cause further friction in already frayed relations with Washington.
He made clear he believed there would be few diplomatic consequences even if it did, dismissing suggestions this would amount to a "Cold War" act.
"It was strange to hear that Snowden is flying to Moscow from Hong Kong as an ordinary passenger. The U.S. wants him very much, but China didn't hand him over," Pushkov wrote on Twitter.
"If spying wearing a wig is the norm, then granting of political refuge is not an act (of the Cold War) either," he wrote, referring to the expulsion of a U.S. diplomat who was accused last month of spying following his detention with wigs, a compass and large sums of money.
People who have taken refuge in Moscow in the past include Lee Harvey Oswald, the man later accused of assassinating President John F. Kennedy. He defected to the Soviet Union in 1959 and returned to the United States in 1962, before Kennedy's murder.
Others include four British double agents during the Cold War - Guy Burgess, Donald Maclean, Kim Philby and George Blake.
Blake was awarded a medal by Putin in 2007 and lives quietly outside Moscow to this day.
(Additonal reporting by Steve Gutterman; Writing by Timothy Heritage; editing by David Stamp)