The founder of the WikiLeaks secret-spilling organization, Julian Assange, insisted he couldn't go into details about where Snowden was, but said he was safe.
Snowden has applied for asylum in Ecuador, Iceland and possibly other countries, Assange said.
An Aeroflot representative who wouldn't give her name told The Associated Press that Snowden wasn't on flight SU150 to Havana, which was filled with journalists trying to track him down. Two AP journalists on the flight confirmed after it arrived Monday evening in Havana that Snowden wasn't on the plane.
Security around the aircraft was heavy prior to boarding and guards tried to prevent the scrum of photographers and cameramen from taking pictures of the plane, heightening speculation that Snowden might have been secretly escorted on board.
In Havana, Cuban officers also clamped down, forcing journalists to move outside the airport building.
The Interfax news agency, which has extensive contacts with Russian security agencies, cited a source as saying Snowden could have flown out in a different plane unseen by journalists.
Others speculated Russian security agencies might want to keep Snowden in Russia for a more thorough debriefing.
Snowden had not been seen since he arrived in Moscow on Sunday from Hong Kong, where he was in hiding for several weeks to evade U.S. justice and left to dodge efforts to extradite him.
After spending a night in Moscow's Sheremetyevo Airport, he had been expected to fly to Cuba and Venezuela en route to possible asylum in Ecuador.
Interfax quoted an unidentified "well-informed source" in Moscow saying that Russia received a U.S. request to extradite Snowden and responded by saying it would consider that. But the same source said Russia could not detain and extradite Snowden since he hadn't technically crossed the Russian border.
Justice Department officials in Washington did not immediately respond to an email seeking comment.
Experts said it was likely that the Russians were questioning Snowden, interested in what he knew about U.S. electronic espionage against Moscow.
"If Russian special services hadn't shown interest in Snowden, they would have been utterly unprofessional," Igor Korotchenko, a former colonel in Russia's top military command turned security analyst, said on state Rossiya 24 television.
U.S. Secretary of State John Kerry said Monday it would be "deeply troubling" if Russia or Hong Kong had notice of Snowden's plans and that would affect their relations with the United States.
The controversy over Snowden could further hurt U.S.-Russian relations, already strained over arguments about Syria and a ban on U.S. adoptions of Russian children.
The Kremlin has previously said Russia would be ready to consider Snowden's request for asylum.
Aeroflot said earlier that Snowden had registered for the flight using his American passport, which the United States recently annulled.
Ecuadorean Foreign Minister Ricardo Patino said his government had received an asylum request, adding Monday that the decision "has to do with freedom of expression and with the security of citizens around the world."
Ecuador has rejected the United States' previous efforts at cooperation, and has been helping Assange avoid prosecution by allowing him to stay at its embassy in London.
But Assange's comments in a telephone conference with reporters that Snowden had applied in multiple places opened other possibilities of where he might try to go.
WikiLeaks has said that it is providing legal help to Snowden at his request and that he was being escorted by diplomats and legal advisers from the group.
Icelandic officials have confirmed receiving an informal request for asylum conveyed by WikiLeaks, which has strong links to the tiny North Atlantic nation. But authorities there have insisted that Snowden must be on Icelandic soil before lodging a formal request.
Snowden gave documents to The Guardian and The Washington Post newspapers disclosing U.S. surveillance programs that collect vast amounts of phone records and online data in the name of foreign intelligence, often sweeping up information on American citizens.
Officials have the ability to collect phone and Internet information broadly but need a warrant to examine specific cases where they believe terrorism is involved.
Snowden had been in hiding for several weeks in Hong Kong, a former British colony with a high degree of autonomy from mainland China.
The United States formally sought Snowden's extradition from Hong Kong to face espionage charges but was rebuffed; Hong Kong officials said the U.S. request did not fully comply with their laws.
The Justice Department rejected that claim, saying its request met all of the requirements of the extradition treaty between the U.S. and Hong Kong.
During conversations last week, including a phone call Wednesday between Attorney General Eric Holder and Hong Kong Secretary for Justice Rimsky Yuen, Hong Kong officials never raised any issues regarding sufficiency of the U.S. request, the Justice Department said.
The United States was in touch through diplomatic and law enforcement channels with countries that Snowden could travel through or to, reminding them that Snowden is wanted on criminal charges and reiterating Washington's position that he should only be permitted to travel back to the U.S., a State Department official said.
U.S. officials spoke on condition of anonymity because they were not authorized to publicly discuss the case.
Caitlin Hayden, a spokeswoman for the National Security Council, said, "Given our intensified cooperation after the Boston marathon bombings and our history of working with Russia on law enforcement matters - including returning numerous high-level criminals back to Russia at the request of the Russian government - we expect the Russian government to look at all options available to expel Mr. Snowden back to the U.S. to face justice for the crimes with which he is charged."
Still, the United States is likely to have problems interrupting Snowden's passage. The United States does not have an extradition treaty with Russia, but does with Cuba, Venezuela and Ecuador. Even with an extradition agreement though, any country could give Snowden a political exemption.
It also wasn't clear Snowden was finished disclosing highly classified information.
Snowden has perhaps more than 200 sensitive documents, Sen. Dianne Feinstein, chairwoman of the Senate Intelligence Committee, said on CBS' "Face the Nation."
Snowden has asked for legal advice from former Spanish judge Baltasar Garzon, the judge's office said Monday. Garzon told The Associated Press earlier that he was considering the case but had yet to speak directly to Snowden.
"Before making any decision in this regard it is my intention to study and assess the case in depth as well as to communicate with Mr. Snowden," Monday's statement read.
Garzon is best known for indicting a totalitarian ruler, former Chilean dictator Augusto Pinochet, in 1998, and trying to put him on trial in Madrid for crimes against humanity.
But has been suspended from office in Spain for starting an investigation into killings committed during the Spanish Civil War and the early years of the Franco dictatorship.