Because Snowden's U.S. passport has been revoked, the logistics of him departing are complicated. Venezuela, Nicaragua and Bolivia have made asylum offers over the past two days, but the three countries haven't indicated they would help Snowden by issuing a travel document, which he would need to leave Russia.
The former NSA systems analyst, who is charged with violating U.S. espionage laws, is believed to be stuck in the transit area of Moscow's main international airport after arriving June 23 from Hong Kong.
Russia doesn't appear willing to help him leave the airport, with Kremlin spokesman Alexei Pavlov saying Saturday the issue of Snowden's travel documents is "not our business." On Monday, President Vladimir Putin said Snowden would be offered asylum in Russia if he stopped leaking U.S. secrets. Snowden then withdrew his Russian asylum bid, a Russian official said.
While President Barack Obama has publicly displayed a relaxed attitude toward Snowden's movements, saying last month that he wouldn't be "scrambling jets" to capture him, other senior U.S. officials have used unusually harsh language that they want him back.
White House spokesman Jay Carney said China had "unquestionably" damaged its relationship with Washington for not returning Snowden, who recently turned 30, from semi-autonomous Hong Kong while he was still there.
"The Chinese have emphasized the importance of building mutual trust," Carney said last month. "We think that they have dealt that effort a serious setback. If we cannot count on them to honor their legal extradition obligations, then there is a problem."
China may be reluctant to further complicate its relationship with the U.S. by allowing Snowden back in Hong Kong, even if only as a transfer point to Latin America.
Snowden has asked for asylum in more than 20 countries and many have turned him down. WikiLeaks, which has been helping Snowden, said Friday he had submitted asylum applications to six new countries, which the secret-spilling website declined to identify "due to attempted U.S. interference."
The asylum offers from Venezuela, Nicaragua and Bolivia came after leftist South American leaders gathered to denounce the rerouting of Bolivian President Evo Morales' plane over Europe amid reports that the fugitive American was aboard.
Spain says it had been warned along with other European countries that Snowden was aboard the Bolivian presidential plane, an acknowledgement the manhunt for the fugitive leaker had something to do with the plane's unexpected diversion to Austria. It is unclear whether Washington warned Madrid about the Bolivian president's plane.
On Saturday, Morales offered asylum to Snowden, but didn't say if Bolivia had received a request from him.
"I want to tell those Europeans and North Americans that as a just protest we now will give asylum to that North American who is persecuted by his compatriots," Morales said during an appearance in the indigenous town of Chipaya.
U.S. officials have declined to comment on the grounding of Morales' plane. They said they won't give details about their conversations with European countries, except to say that they have stated Washington's general position that it wants Snowden back.
Snowden, who on Saturday afternoon wasn't on an Interpol list of people for whom international arrest warrants have been issued, had booked a seat on a Havana-bound flight on June 24, but never made it.
Direct Havana flights, operated by Aeroflot from Moscow's main airport five times a week, are the easiest option of reaching Latin America from Moscow. But the Moscow-Havana's travel path passes over mainland U.S., raising the chances of it being grounded. There are other routes, but there is no assurance he'd have free passage.
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