The US has criticised Russia and China after fugitive Edward Snowden left Hong Kong for Moscow.
President Barack Obama said the US was pursuing "all the appropriate legal channels" in pursuit of him.
US Secretary of State John Kerry has said it would be "disappointing" if Russia and China had helped him evade an attempt to extradite him.
Mr Snowden, who has applied for asylum in Ecuador, is believed to still be in Russia having flown there on Sunday.
White House spokesman Jay Carney said he did not believe Hong Kong's reasons for letting him leave.
The US has revoked Mr Snowden's passport, and he is thought to have spent the night in an airside hotel at Moscow's Sheremetyevo airport.
On Monday, a seat was booked in his name on a flight to Cuba, but he was not seen on board when it took off.
The 30-year-old IT expert is wanted by the US for revealing to the media details of a secret government surveillance programme, which he obtained while working as a contractor for the National Security Agency (NSA).
He is charged with theft of government property, unauthorised communication of national defence information and wilful communication of classified communications intelligence.
Mr Obama briefly mentioned the case at the White House on Monday, telling reporters: "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."
Speaking during a visit to India earlier, Mr Kerry said it would be "deeply troubling" if it became clear that China had "wilfully" allowed him to fly out of Hong Kong.
20 May: Snowden flies from Hawaii to Hong Kong.
5 June: From Hong Kong, Snowden discloses details of what he describes as a vast US phone and internet surveillance programme to the UK's Guardian newspaper.
23 June: Snowden leaves Hong Kong on a flight to Moscow. He is currently thought to remain airside at Sheremetyevo airport.
From Moscow, Snowden could fly to Cuba, en route to Ecuador, which has said it is "analysing" whether to grant him asylum.
Venezuela had also been considered a possible destination for Snowden, however it is thought he would only pass through on his way to Ecuador.
Snowden is reported to have requested asylum in Ecuador, which previously granted haven to Wikileaks founder Julian Assange in its London embassy.
"There would be without any question some effect and impact on the relationship and consequences," he said.
He also called on Russia to "live by the standards of the law because that's in the interests of everybody".
Later, Mr Carney said: "It is our understanding that he is still in Russia."
In strongly worded comments at a news conference, he said Washington was "just not buying" Hong Kong's assertion that the US extradition papers were not in order so they had no reason to detain Mr Snowden.
"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," he said.
He added that senior US officials were briefing President Barack Obama regularly about all the developments, and called on Russia to use all options to expel the former US spy agency contractor.
Meanwhile, Russia's Interfax state news agency quoted an informed source as saying Moscow was considering a US extradition request, but that Mr Snowden had not officially crossed the Russian border so could not be detained.
'Use all options'
Mr Snowden was in hiding in Hong Kong when his leaks were first published.
During a visit to Vietnam earlier on Monday, Ecuador's Foreign Minister Ricardo Patino read out a letter Mr Snowden had sent to request asylum, in which he said he was "at risk of being persecuted by the US and its agents".
Mr Patino confirmed that his country was processing an asylum request from Mr Snowden.
Quito was in contact with Moscow who could "make the decision it feels is most convenient in accordance with its laws and politics and in accordance with the international laws and norms that could be applied to this case", he said.
When asked whether he knew of Mr Snowden's current location, he declined to answer.
"We will consider the position of the US government and we will take a decision in due course," he said, saying Ecuador put the protection of human rights "above any other interest".
The US and Ecuador have a joint extradition treaty, but it is not applicable to "crimes or offences of a political character".
Mr Snowden is being supported by the whistleblowing website Wikileaks, which said on Sunday that he was heading to Ecuador accompanied by some of its diplomats and legal advisers.
Ecuador is already giving political asylum at its London embassy to Wikileaks founder Julian Assange, who is wanted for questioning in Sweden over allegations of sexual assault - which he denies.
On Monday, Mr Assange said Mr Snowden was "healthy and safe", and travelling to Ecuador "via a safe path through Russia and other states".
He said Mr Snowden had left Hong Kong on a refugee document of passage issued by Ecuador, and was not carrying any NSA secrets with him.
Mr Snowden's leaks have led to revelations that the US is systematically seizing vast amounts of phone and web data under an NSA programme known as Prism.
He earlier said he had decided to speak out after observing "a continuing litany of lies" from senior officials to Congress.
US officials have defended the practice of gathering telephone and internet data from private users around the world.
They say Prism cannot be used to intentionally target any Americans or anyone in the US, and that it is supervised by judges.