Snowden, who is stranded at the Moscow airport for more than two weeks, today said he would prefer to seek asylum in Russia.
"Our position on Mr Snowden is that there are felony charges against him and our belief that he ought to be returned to the United States to face those felony charges is as it was. We have communicated it to a variety of countries, including Russia," White House Press Secretary Jay Carney told reporters at his daily news conference.
"But having said that our position also remains that we don't believe this should and we don't want it to do harm to our important relationship with Russia, and we continue to discuss with Russia our strongly-held view that there is an absolute legal justification for him to be expelled, for him to be returned to the United States to face the charges that have been brought against him for the unauthorised leaking of classified information," he said.
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"We are working with the Russians and have made clear to the Russians our views about the fact that Mr Snowden has been charged with very serious crimes and that he should be returned to the United States, where he will be granted full due process and every right available to him as a United States citizen facing our justice system under the Constitution," he said.
US President Barack Obama was scheduled to call his Russian counterpart Vladimir Putin, he said, adding he expects this issue to come up.
Carney said during the just concluded US-China Strategic and Economic Dialogue, the US made it clear to the Chinese officials that their handling of the Snowden affair was not consistent with the relationship between the two countries.
"At the US-China Strategic and Economic Dialogue this week we made clear that China's handling of this case was not consistent with the spirit of Sunnylands or with the type of relationship, the new model, that we both seek to build," he said.
The issue was raised by Deputy Secretary William Burns, he said.
"We were very disappointed with how the authorities in Beijing and Hong Kong handled the Snowden case, which undermined our effort to build the trust needed to manage difficult issues," Carney said.