Google's David Drummond: "We do not provide indirect access, there's no drop box, no back door"
Google, Facebook and Microsoft have asked the US government to allow them to disclose the security requests they receive for handing over user data.
The move comes after recent reports claimed that US authorities had direct access to the servers of nine major US tech firms, including Google and Apple.
Google said the claims were "untrue" but added that nondisclosure rules of such requests "fuel that speculation".
The US has confirmed that the surveillance programme exists.
But it is coming under increasing pressure from many different quarters to end the practice.
The American Civil Liberties Union filed a lawsuit on Tuesday, challenging the legality of the programme.
Separately, a coalition of more than 80 rights groups and internet companies have launched a website, StopWatching.Us, which has called on Congress to launch a full investigation.
The site is backed by the World Wide Web Foundation, a group founded by Tim Berners-Lee, the inventor of the Web.
David Drummond, chief legal officer of Google has written to the US Attorney General seeking permission to publish "aggregate numbers of national security requests, including Foreign Intelligence Surveillance Act (Fisa) disclosures".
"Google's numbers would clearly show that our compliance with these requests falls far short of the claims being made. Google has nothing to hide," he said in the letter.
Microsoft said that greater transparency on the requests "would help the community understand and debate these important issues''.
Ted Ullyot, Facebook's general counsel, said the social networking leader wants to provide "a complete picture of the government requests we receive, and how we respond".
The surveillance programme, known as Prism, came to light last week after a series of leaks by former CIA employee Edward Snowden.
Mr Snowden told the Guardian that operatives had the power to tap into anyone's emails at any time.
"We can plant bugs in machines. Once you go on the network, I can identify your machine. You will never be safe whatever protections you put in place," he was quoted as saying by the Guardian.
Major US technology firms have denied giving such unfettered access to US authorities.
However, US officials have defended the programme, saying it is authorised under Fisa.
One of the Guardian journalists who wrote the Prism stories, Glenn Greenwald, has promised "more significant revelations".
Traitor or hero?
Mr Snowden's leaks have triggered concerns over rights of online users.
The European Union has sought assurance that Europeans' rights are not being infringed by the newly-revealed US surveillance programmes.
Justice Commissioner Viviane Reding tweeted: "This case shows why a clear legal framework for the protection of personal data is not a luxury but a necessity."
Meanwhile, there is also a debate going on whether Mr Snodwen's decision to reveal the programme was a right move.
In the US, Mitch McConnell, the top Republican in the Senate, said the person responsible for the leak should be prosecuted to the fullest extent of the law.
He said privacy concerns were understandable given the scope of the programmes, but added it was hard to comprehend why Mr Snowden would give information to enemies of the US.
Dianne Feinstein, a Democrat who chairs the Senate intelligence committee, accused Mr Snowden of "treason" and said the American authorities were "aggressively" pursuing him.
The top Republican in the US House of Representatives, Speaker John Boehner, also labelled Mr Snowden a "traitor".
However, anti-secrecy activist and WikiLeaks founder Julian Assange lent his support to Mr Snowden.
"Edward Snowden is a hero who has informed the public about one of the most serious events of the decade, which was the creeping formulation of a mass surveillance state," Mr Assange was quoted as saying by the AFP news agency.