Snowden, who has admitted leaking data about the National Security Agency's cellphone and Internet surveillance programs, is under a U.S. indictment for stealing and leaking classified documents.
Putin, speaking in Finland Tuesday, acknowledged Snowden is in the transit zone of Moscow's Sheremetyevo Airport.
He said Snowden's arrival at the airport "came as a surprise" to Russian officials, Russia Today reported.
"He arrived as a transit passenger, and didn't need a [Russian] visa, or any other documents," Putin said. "As a transit passenger he is entitled to buy a ticket and fly to wherever he wants."
He said Snowden has not crossed the border into Russia and it would not be possible for Russia to extradite Snowden to the United States in any case since the two countries do not have an extradition treaty.
"I hope this won't affect the cordial nature of our relations with the U.S.," Putin said.
"Snowden is a free person," he said. "The sooner he chooses his final destination, the better it is for him and Russia."
Hong Kong's South China Morning Post reported Monday Snowden told it he specifically sought the job at U.S. defense contractor Booz Allen Hamilton Inc. so he could collect information about the NSA's secret surveillance programs to release to the news media.
"My position with Booz Allen Hamilton granted me access to lists of machines all over the world the NSA hacked," he said in a June 12 interview. "That is why I accepted that position about three months ago."
Russian Foreign Minister Sergei Lavrov had said previously Snowden had not crossed the border into Russia.
"I want to say right away that we have nothing to do with Snowden, or with his attitude to the American legal system, or with his movements around the world," Sergei Lavrov told a news conference. "He chose his own route, and we found out about it -- like most people here -- from the media."
Media reported Monday Snowden flew to Sheremetyevo International Airport Sunday but had gone no further than the transit area because he did not have a Russian visa, RIA Novosti reported. Staying in the transit zone of an airport does not constitute crossing the country's border.
Putin said Tuesday dealing with issues such as the Snowden case "is like shearing a pig: there's lots of squealing and little fleece."
U.S. officials said talks were under way with Moscow, and U.S. officials believe the Kremlin was taking the matter "seriously."
"We have a strong law enforcement cooperative relationship with the Russians, and that relationship has resulted in that past in us returning criminals to Russia," Carney said Monday.
"We are expecting the Russians to examine the options available to them to expel Mr. Snowden for his return to the United States," he said.
U.S. Secretary of State John Kerry called on Russia Monday to expel Snowden.
"I would urge them to live by the standards of the law, because that's in the interest of everybody," Kerry said.
Lavrov suggested Kerry's comment was an "absolutely ungrounded and unacceptable" attempt to "accuse Russia of violation of U.S. laws and even some sort of conspiracy."
"There are no legal grounds for such conduct of U.S. officials," Lavrov said.
Kerry said Tuesday in Jidda, Saudi Arabia, the United States is "not looking for a confrontation."
Speaking at a news conference with Saudi Foreign Minister Prince Saud al-Faisal, said Washington is "not ordering" other governments to return Snowden to the United States for trial on espionage charges.
"We are simply requesting under a very normal procedure for the transfer of somebody," he said.
Kerry said Monday there is irony in Snowden seeking refuge in China and Russia.
"I wonder if Mr. Snowden chose China and Russia as assistants in his flight from justice because they're such powerful bastions of Internet freedom," Kerry said during a stop in New Delhi.
The Obama administration Monday questioned whether China was living up to legal obligation on extradition and official Chinese government media Tuesday mocked Washington's indignation.
"The Chinese have emphasized the importance of building mutual trust," White House spokesman Jay Carney said Monday during a media briefing. "And 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."
In Beijing, the People's Daily, the official newspaper of the highest authority within China's Communist Party, said Tuesday: "If Snowden had been a Chinese man, President Obama would certainly have invited him to a White House dinner. President Obama would have nominated him for the Nobel Peace Prize ... for defending freedom and human rights."
A separate commentary said Snowden's "fearlessness ... tore off Washington's self-righteous facade."
Officials in Ecuador said they were considering Snowden's application for asylum.
The United States is Ecuador's leading trading partner, accounting for nearly $11 billion, or 43 percent, of its exports, The Wall Street Journal reported.
A key U.S.-Ecuador trade preference measure expires next month. If Ecuador grants asylum to Snowden, U.S. lawmakers could retaliate by refusing to renew it, administration officials told the Journal.