Edward Snowden, the former CIA technician who blew the whistle on global surveillance operations, has opened a new front against the US authorities, claiming they hacked into Chinese mobile phone companies to access millions of private text messages.

His latest claims came as US officials, who have filed criminal charges against him, warned Hong Kong to comply with an extradition request or risk complicating diplomatic relations after some of the territory's politicians called for Snowden to be protected.

The latest developments will raise fears that the US's action may have pushed Snowden into the hands of the Chinese, triggering what could be a tense and prolonged diplomatic and legal wrangle between the world's two leading superpowers.

Snowden, whose whereabouts have not been publicly known since he checked out of a Hong Kong hotel on 10 June, was reported by the Chinese media on Saturday to be in a "safe place" in the former British colony.

The 30-year-old intelligence analyst has over the past three weeks leaked a series of documents to the Guardian revealing how US and UK secret services gain access to huge amounts of phone and internet data, raising serious questions about privacy in the internet age.

On Friday, based on documents from Snowden, the Guardian reported that Britain's spy agency GCHQ has secretly gained access to the network of cables carrying the world's phone calls and internet traffic, without the authorities having made this known to the public. It was also reported that GCHQ is processing vast streams of sensitive information which it is sharing with its US partner, the National Security Agency.

On Saturday the former British foreign secretary Sir Malcolm Rifkind, who now chairs the intelligence and security committee, said the committee would launch an investigation into the latest revelations. The committee will receive an official report from GCHQ about the story within days and will then decide whether to call witnesses to give oral evidence. If it is then thought necessary, the committee can require GCHQ to submit relevant data.

Within hours of news breaking that the US had filed charges against Snowden, the South China Morning Post reported that the whistleblower had handed over a series of documents to the paper detailing how the US had targeted Chinese phone companies as part of a widespread attempt to get its hands on a mass of data.

Text messaging is the most popular form of communication in mainland China where more than 900bn SMS messages were exchanged in 2012.Snowden reportedly told the paper: "The NSA does all kinds of things like hack Chinese cellphone companies to steal all of your SMS data."

The paper said Snowden had also passed on information detailing NSA attacks on China's prestigious Tsinghua University, the hub of a major digital network from which data on millions of Chinese citizens could be harvested.

As Snowden made his latest disclosures, the US issued an extradition request to Hong Kong and piled pressure on the territory to respond swiftly. "If Hong Kong doesn't act soon, it will complicate our bilateral relations and raise questions about Hong Kong's commitment to the rule of law," a senior Obama administration official said.

Snowden appeared to be gaining support from politicians in Hong Kong who said China should support him against any extradition application from the US, which on Friday charged him under its Espionage Act. One legislator, Leung Kwok-hung, said Beijing should issue instructions to protect Snowden from extradition before his case was dragged through the courts. Leung urged the Hong Kong people to "take to the streets to protect Snowden". Another politician, Cyd Ho, vice-chairwoman of the pro-democracy Labour party, said China "should now make its stance clear to the Hong Kong SAR [Special Administrative Region] government" before the case goes before a court.

China has urged Washington to provide explanations following Snowden's disclosures that NSA programs collect millions of telephone records and track foreign internet activity on US networks. In a press conference Hong Kong's police commissioner, Andy Tsang, indicated that the normal legal process would be followed after the US filed criminal charges. "All foreign citizens must comply with Hong Kong's law," he said, adding that the police would act on the request once it was received.

He declined to comment on reports in one Hong Kong newspaper that Snowden is already in a police safe house.

In response to the Guardian's latest revelations regarding the surveillance activities of GCHQ, politicians and freedom of information campaigners raised concerns about the lack of oversight and up-to-date laws with which to monitor and regulate the activities of the secret services. Former Foreign Office minister David Davis MP said documents containing an admission by GCHQ lawyers that UK oversight was "light" compared with that in the US were particularly worrying.

"This reinforces the view that the oversight structure is wholly inadequate. Really what is needed is a full-scale independent judicial oversight that reports to parliament."

Shami Chakrabarti, the director of Liberty, said: "It's possible to be shocked but not surprised at this blanket surveillance on a breathtaking scale. The authorities appear to be kidding themselves with a very generous interpretation of the law that cannot stand with article 8 of the European convention on human rights.

"To argue this isn't snooping because they haven't got time to read all this private information is like arguing we'd all be comfortable with our homes being raided and our private papers copied – as long as the authorities stored them in sealed plastic bags."

Carl Miller, director for social media at the thinktank Demos, said: "Just like the rest of us, terrorists and criminals are increasingly using social media and other forms of online communication. So it's clear that the intelligence services should be able to access this where it is necessary and proportionate. But this is the crucial point. What these latest stories reveal is that much of this surveillance is happening already, but without the security services having made the public argument for these powers. There is a clear need for a legal grounding or oversight structure that commands public confidence."