The White House pressured Russia to expel fugitive US leaker Edward Snowden on Monday and warned China it had undermined efforts to rebuild trust by allowing him to leave Hong Kong.

President Barack Obama, meanwhile, said Washington was using every legal channel to apprehend Snowden, the self-confessed source of explosive leaks detailing the extent of covert US spy agency phone and Internet surveillance.

White House spokesman Jay Carney said Washington assumed that Snowden was still in Moscow, where he went after slipping out of Hong Kong, and lashed out at Beijing for letting him go, despite US extradition requests.

"With regards to ... the Chinese government, we are just not buying that this was a technical decision by a Hong Kong immigration official," he said.

"This was a deliberate choice by the government to release a fugitive despite a valid arrest warrant, and that decision unquestionably has a negative impact on the US-China relationship."

Carney noted that Beijing, as evidenced by Obama's summit with new president Xi Jinping this month in California, had been seeking to rebuild trust with Washington.

"We think that they have dealt that effort a serious setback. If we cannot count on them to honor their legal extradition obligations, then there is a problem. And that is a point we are making to them very directly."

Carney also told reporters the White House believes Russia should accept a request for Snowden to be expelled back to the United States.

"We do expect the Russian government to look at all the options available to them to expel Mr Snowden back to the United States," he said.

As part of intense US pressure on Russia, FBI chief Robert Mueller was in touch twice on Monday with his counterpart in Russia, an official said.

Carney also noted intensified cooperation on law enforcement with Russia after the Boston bombings and had said Washington had returned "numerous high-level criminals" at the request of the Russian government."

He refused to speculate on the implications of any failure by Russia to hand over Snowden, who was last believed to be in a transit area of Moscow airport.

He also said Washington had been in touch with countries through which Snowden might transit, noting that he was a fugitive from felony charges in the United States. His US passport has been revoked.

Obama, after meeting businessmen at the White House to discuss immigration reform, declined to be say whether he had contacted Russian President Vladimir Putin, whom he met a week ago in Northern Ireland.

"What we know is that we are following all the appropriate legal channels and working with various other countries to make sure that the rule of law is observed," Obama told reporters.

The president then deferred to the US Justice Department on the issue.

Patrick Ventrell, a State Department spokesman, said the administration had been in touch with Ecuador, which has said Snowden has asked for asylum.

As intrigue mounted, Snowden vanished in Moscow after failing to take a flight to Cuba on which he was booked -- possibly on a journey scheduled to end up in Ecuador.

He was said by Russian officials to have spent Sunday night in a "capsule hotel" at Moscow's Sheremetyevo airport awaiting his onward connection.

In New Delhi, US Secretary of State John Kerry also voiced hope that Russia has reconsidered allowing Snowden to fly out.

"We continue to hope that the Russians will do the right thing," Kerry told NBC News.

"We have very high hopes that the Russians, who've said they want to cooperate and have a strong relationship with us, will understand that this is important," he said.

"I hope it's a good sign he isn't on that flight," he said.

Interfax quoted a source close to the matter as saying Russia was studying an extradition request from the United States for Snowden.

However, the source said Russia does not have the right to either "detain or deport" Snowden because he has not officially crossed the Russian border.