Snowden was charged by Washington with espionage and theft of government property following his disclosure of massive secret phone and internet surveillance programmes of the US National Security Agency.
"Our position on Mr Snowden and the 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, and we have communicated it to a variety of countries, including Russia," Xinhua quoted White House spokesman Jay Carney as saying at a press briefing.
"We continue to discuss with Russia our strongly held view that there is 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," Carney added.
Earlier in the day, Snowden, who has been marooned in the transit zone of Moscow's Sheremetyevo airport since his arrival there June 23, met a group of Russian and foreign human rights activists, lawyers and parliamentarians.
Several participants in the closed-door talks confirmed that Snowden was seeking asylum in Russia.
Russian lawmaker Vyacheslav Nikonov said the 30-year-old American has accepted the Kremlin's condition that he must stop damaging US interests if he wants to stay in Russia.
The US State Department has revoked his passport, making it difficult for him to travel to other destinations without the document.
Carney Friday criticised Russia for allowing Snowden to meet human rights activists.
"I would simply say that providing a propaganda platform for Mr Snowden runs counter to the Russian government's previous declarations of Russia's neutrality and that they have no control over his presence in the airport," Carney said.
"It's also incompatible with Russian assurances that they do not want Mr Snowden to further damage US interests."
He said Washington does not want to see bilateral ties with Moscow harmed by the Snowden case.
Meanwhile, US State Department spokeswoman Jen Psaki also expressed disappointment with the Snowden meeting, a move she said was facilitated by Russia.
"We obviously don't think this was a proper forum or a proper elevation of him," she said.
"He's not a whistleblower. He's not a human rights activist. He's wanted on a series of serious criminal charges."
"We still believe that Russia has the opportunity to do the right thing and facilitate his return to the United States," she added.