Minutes after President Barack Obama said that the U.S. has held "high level" discussions with Russia about NSA leaker Edward Snowden's extradition, Russian President Vladimir Putin said Russia would "never" hand him over.

Reuters reports that Putin also said that if Snowden wants to stay in Russia, he must "stop his work aimed at harming our American partners" in leaking secret information about the National Security Agency's surveillance programs.

"There is one condition if he wants to remain here: He must stop his work aimed at damaging our American partners. As odd as it may sound from me," Putin said at a press conference.

Meanwhile, WikiLeaks founder Julian Assange said Sunday that there would be "no stopping" publication of information gathered by Snowden.

"Great care has been taken to make sure that Mr. Snowden can't be pressured by any state to stop the publication process," Assange said on ABC's "This Week."

Putin said he wouldn't hand over Snowden because Russia has never extradited anyone.

Snowden has been in Russia for more than a week after leaving Hong Kong last Sunday — a move that strained relations between the U.S. and China. The White House warned Russia last week to "expel Mr. Snowden without delay," saying there was a "clear legal basis" to do so.

The Los Angeles Times reported Monday that Snowden met with Russian diplomatic officials in the morning with an appeal for asylum in 15 different countries. Russia is one of the countries on the list, the New York Times reported, citing a Russian immigration official.

It's unclear what other countries are on that list, but Snowden's appeal came one day after Ecuador President Rafael Correa backed away from suggestions that his country would provide Snowden with asylum.