The United States will hold talks with Russia's defence and foreign ministers in Washington on Friday despite Moscow's decision to grant asylum to former US spy agency contractor Edward Snowden.

The State Department said the talks would go ahead and that Snowden's case would be among the issues raised when US Secretary of State John Kerry and Defence Secretary Chuck Hagel meet their Russian counterparts.

Snowden had spent more than five weeks in a Moscow airport while trying to find a country to take him in. The US wanted him returned to face charges for leaking National Security Agency surveillance secrets to the media.

"We have raised Mr Snowden with Russian officials many times in recent weeks. We expect to do so again," State Department spokeswoman Jen Psaki told reporters.

"We would like to see Mr Snowden return to the United States. I don't know technically what that requires but we know they have the capability to do that."

Snowden asylum

Moscow's rejection of US pleas to hand over Snowden and grant him a year's asylum on Thursday has prompted President Barack Obama to rethink whether to hold a summit in Moscow with Russian President Vladimir Putin next month.

The US administration questions further bilateral contact at the highest level... this an utter distortion of reality. Sergei Ryabkov, Russian deputy foreign minister

Snowden's asylum in Russia also had put into doubt this week's so-called "two-plus-two" talks between the Russian and US officials.

The US appears to be trying to avoid derailing ties with its former Cold War rival by proceeding with some high-level talks with Russia while still leaving Obama's participation in the summit in doubt.

Worsened ties between the US and Russia could make it even more difficult for the two nations to arrange any kind of political solution in Syria, for example.

There are also concerns in Washington that Russia may break ranks with Western countries seeking to curb Tehran's nuclear ambitions through tough sanctions.

Psaki said Syria would be part of the conversation, as well as Iran's nuclear programme, and Russia's support of US efforts to move material in and out of landlocked Afghanistan as the US winds down a war of nearly 12 years there.

Russian deputy foreign minister Sergei Ryabkov criticised perceived US wobbling on the need for top-level contact between the two countries.

"The US administration questions further bilateral contact at the highest level [due to the situation with Snowden]," Ryabkov was quoted as saying by Interfax. "It seems to me that this an utter distortion of reality. This is viewing the world through a distorted lens."