Earlier, he said he had an “obligation to help free people from oppression”. It emerged last week that US agencies were gathering millions of phone records and monitoring internet data.
A spokesman for the US Office of the Director of National Intelligence said the case had been referred to the Department of Justice as a criminal matter.
Meanwhile a petition posted on the White House website, calling for Mr Snowden’s immediate pardon, has gathered more than 30,000 signatures.
He was revealed as the source of the leaks at his own request by the UK’s Guardian newspaper.
Hong Kong’s broadcaster RTHK said Mr Snowden checked out of the Mira hotel on Monday. Reuters news agency quoted hotel staff as saying that he had left at noon. Ewen MacAskill, a Guardian journalist, told the BBC he believed Mr Snowden was still in Hong Kong.
Hong Kong – a Chinese territory – has an extradition treaty with the US, although analysts say any attempts to bring Mr Snowden to America may take months and could be blocked by Beijing.
Mr Snowden is believed to have arrived in Hong Kong on 20 May. A standard visa on arrival in the territory for a US citizen lasts for 90 days.
His revelations have caused transatlantic political fallout, amid allegations that the UK’s electronic surveillance agency, GCHQ, used the US system to snoop on British citizens.
Foreign Secretary William Hague cancelled a trip to Washington to address the UK parliament on Monday and deny the claims.
Mr Snowden is described by the Guardian as an ex-CIA technical assistant, currently employed by Booz Allen Hamilton, a defence contractor for the US National Security Agency (NSA).
He told the newspaper: “The NSA has built an infrastructure that allows it to intercept almost everything. With this capability, the vast majority of human communications are automatically ingested without targeting.
“If I wanted to see your emails or your wife’s phone, all I have to do is use intercepts. I can get your emails, passwords, phone records, credit cards.
“I don’t want to live in a society that does these sort of things. I do not want to live in a world where everything I do and say is recorded.”
Here is the interview if you haven’t watched it: