MOSCOW—National Security Agency leaker and U.S. fugitive Edward Snowden appeared to be stuck Tuesday in a bleak airport terminal here, with Russian President Vladimir Putin urging him to get on his way.

Mr. Putin shot down a request by American officials to expel Mr. Snowden, the 30-year-old former security contractor wanted by U.S. authorities for leaking information about domestic surveillance operations.

The Russian president described Mr. Snowden's arrival in Moscow on a Sunday flight from Hong Kong as a "complete surprise" and said he remained in the airport's transit zone.

"Mr. Snowden is a free man and the sooner he chooses his final destination, the better it will be for us and him," he said at a news conference during an official trip to Finland. When asked about handing Mr. Snowden to U.S. authorities, Mr. Putin noted that there is no extradition agreement between Russia and the U.S. Mr. Snowden hadn't crossed Russia's border and was in a "transit hall" for passengers with layovers, he said.

Mr. Putin's comments broke nearly two days of official obfuscation among Russian authorities about Mr. Snowden's whereabouts and heightened the drama in a global showdown that involves the U.S., Russia, China and a former Booz Allen Hamilton contractor who is now one of America's most high-profile fugitives.