State Department spokeswoman Jen Psaki said it would raise concerns in the US-Russian relationship if Moscow were to accept an asylum request from Snowden.

"However we are not at that point yet. They still have the opportunity to do the right thing and return Mr Snowden to the United States and that's what our hope is," she told reporters.

The White House and the State Department complained that the Russian government had permitted Snowden to meet with human rights groups at the Moscow airport. Snowden told activists on Friday he was seeking temporary asylum in Russia and had no regrets about spilling US spy secrets.

"Providing a propaganda platform for Mr Snowden runs counter to the Russian government's previous declarations of Russia's neutrality," Carney said.

He said it was "also incompatible with Russian assurances that they do not want Mr Snowden to further damage US interests."

In Moscow, Putin's spokesman repeated earlier conditions that Snowden should stop harming the interests of the United States if he wants asylum.

The drama has tested US-Russian relations, although no lasting damage has been apparent so far.

"My sense is that both Washington and Moscow have lots of experience in compartmentalizing these kinds of issues when you've got spies or  defectors," said Steven Pifer, a Russia expert who is director of the Brookings Institution's Arms Control Initiative. "They can fence that off from the rest of the relationship."

Related stories:

Snowden seeks political asylum in Russia

Snowden meets Russian human rights groups

Snowden is likely Venezuela bound

3 Latin American leaders offer Snowden asylum

Special:

US surveillance program exposed