(CBS NEWS/AP) -- The bizarre journey of Edward Snowden is far from over. After spending a night in Moscow's airport, the former National Security Agency contractor and admitted leaker of U.S. state secrets was expected to fly to Cuba and Venezuela en route to possible asylum in Ecuador.
But the U.S. says Moscow should hand Snowden over to Washington.
Multiple reports say Snowden wasn't on an Aeroflot flight from Moscow to Havana Monday that earlier reports indicated he'd be on.
Snowden, also a former CIA technician, fled Hong Kong on Sunday to dodge U.S. efforts to extradite him on espionage charges. Ecuador's Foreign Minister, Ricardo Patino, said his government had received an asylum request. He added Monday that Ecuador's decision about the request involves "freedom of expression and ... the security of citizens around the world." He did not say how long it would take Ecuador to decide.
The anti-secrecy group WikiLeaks has said it was helping Snowden.
Ecuador has rejected the United States' previous efforts at cooperation, and has been helping WikiLeaks founder Julian Assange avoid prosecution by allowing him to stay at its embassy in London.
Snowden was on a flight from Hong Kong that arrived in Moscow Sunday and was booked on a flight to Cuba Monday, the Russian news agencies ITAR-Tass and Interfax reported, citing unnamed airline officials.
Patino said, "We know that he's currently in Moscow, and we are ... in touch with the highest authorities of Russia."
The NSC issued a statement early Monday saying it is "disappointed by the decision of the authorities in Hong Kong to permit Mr. Snowden to flee despite the legally valid U.S. request to arrest him for purposes of his extradition under the U.S.-Hong Kong Surrender Agreement. We have registered our strong objections to the authorities in Hong Kong as well as to the Chinese government through diplomatic channels and noted that such behavior is detrimental to U.S.-Hong Kong and U.S.-China bilateral relations."
The statement continued, "We now understand Mr. Snowden is on Russian soil. 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."
At a news conference in New Delhi, India Monday, U.S. Secretary of State John Kerry said Moscow should send Snowden back to the U.S. but, "Historically, there are some countries that just play outside of that process."
Kerry said it would be "very disappointing" if China and Russia allowed Snowden to fly, and there would undoubtedly be "an impact on our relations."
Kerry added that Snowden "places himself above the law, having betrayed his country."
The Reuters news agency quotes a spokesperson for Russian President Vladimir Putin as saying the Kremlin doesn't know of any contact between Snowden and Russian authorities. Reuters says Dmitry Peskov declined to comment on the U.S. calls for Russia to expel Snowden.
A senior administration official told CBS News, "Mr. Snowden's claim that he is focused on supporting transparency, freedom of the press and protection of individual rights and democracy is belied by the protectors he has potentially chosen: China, Russia, Cuba, Venezuela and Ecuador. His failure to criticize these regimes suggests that his true motive throughout has been to injure the national security of the U.S., not to advance internet freedom and free speech."
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 its 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, a Justice representative 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 Snowden should only be permitted to travel back to the U.S., a State Department official said. Snowden's U.S. passport has been revoked.
U.S. officials spoke on condition of anonymity because they were not authorized to publicly discuss the case.
An unidentified Aeroflot airline official was cited by Russia's state ITAR-Tass news agency and Interfax as saying Snowden was on the plane that landed Sunday afternoon in Moscow. The Russian report said Snowden intended to fly to Cuba on Monday and then on to Caracas, Venezuela.
The White House was hoping to stop Snowden before he left Moscow.
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.
The likelihood that any of these countries would stop Snowden from traveling on to Ecuador seemed remote. While diplomatic tensions have thawed in recent years, Cuba and the United States are hardly allies after a half-century of distrust. Another country that could see Snowden pass through, Venezuela, could prove difficult, as well. Former President Hugo Chavez was a sworn enemy of the United States and his successor, Nicolas Maduro, earlier this year called President Obama the "grand chief of devils." The two countries do not exchange ambassadors.
Snowden's options aren't numerous, said Assange's lawyer, Michael Ratner.
"You have to have a country that's going to stand up to the United States," Ratner said. "You're not talking about a huge range of countries here."
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."