"He must stop his work aimed at harming our American partners, as strange as that sounds coming from my lips," he told reporters in Moscow. "He must choose a country of destination and go there. Unfortunately, I don't know when this will happen."
Putin said Russia was not working with Snowden but also did not plan to give him to the United States.
On Tuesday, Russia also said that Snowden had applied for asylum in 15 countries, not 21 as had been claimed by anti-secrecy website WikiLeaks a day earlier. There was no immediate explanation for this discrepancy.
The U.S. does not have an extradition treaty with Russia, but President Barack Obama has noted that Snowden traveled to Moscow without legal papers and referred to "high-level" discussions between the two countries about the case.
"We are hopeful that the Russian government makes decisions based on the normal procedures regarding international travel and the normal interactions that law enforcement have," Obama said.
(Read More: Putin:
SnowdenShould Stop Harming 'Our American Partners')
It was thought that Snowden would eventually head for Ecuador, but the president of the South American country said this week that no asylum request was sent and suggested Russia would make the call on when Snowden could leave and where he would go.
Also on Tuesday, Venezuelan President Nicolas Maduro said Snowden had not applied for asylum in that country, although he added the world community should support the former CIA contractor's work exposing "the imperialist elite of the United States."
"They spy on friend and foe," he told reporters after a gas exporters' conference in Russia. "They have created a semi-Orwellian system."
In a statement released late Monday through WikiLeaks, Snowden said the White House was pressuring other countries to deny him asylum.
"The Obama administration has now adopted the strategy of using citizenship as a weapon," his statement said. "This kind of deception from a world leader is not justice, and neither is the extralegal penalty of exile. These are the old, bad tools of political aggression. Their purpose is to frighten, not me, but those who would come after me."
Countries' Reactions to Snowden's Asylum Applications
Former U.S. spy agency contractor Edward Snowden has applied for political asylum in more than a dozen countries. The 30-year-old American remains in a legal limbo in the transit area at Moscow's Sheremetyevo Airport. He has no legal travel documents and has made his asylum applications through a legal representative.
Here is a list of the countries where Snowden has asked for asylum, as published by WikiLeaks, and their reactions so far.
APPLICATIONS VALID ONLY IF MADE ON THEIR SOIL
WILLING IN PRINCIPLE
Venezuela (has taken no official decision, but president expressed support)
Russia (Snowden has withdrawn his asylum application)
—By Jim Maceda and F. Brinley Bruton, NBC News; Reuters and The Associated Press contributed to this report.