Google has called on the secretive Foreign Intelligence Surveillance Court to relax its gag order on tech companies targeted in US security investigations.

The search giant stepped up its campaign for greater transparency from the US courts Tuesday in the wake of the disclosure of the National Security Agency's top-secret Prism surveillance program.

The legal filing cites the first amendment's guarantee of free speech and follows on from a letter to attorney general Eric Holder asking for permission to disclose the number of requests Google receives under the foreign intelligence securities act (Fisa).

Those requests, targeted at people outside the US, are dealt with in secrecy by a dedicated court. Google is seeking permission to publish the total numbers of requests the Fisa court makes and the numbers of user accounts they affect.

The search firm already publishes a widely imitated "transparency report" that documents demands from the US government and from other governments worldwide. The report documents criminal requests and national security letters, which the government uses to gather information about US citizens in the US. But Google and its peers are barred from disclosing the number of Fisa requests they receive.

"Greater transparency is needed, so today we have petitioned the Foreign Intelligence Surveillance Court to allow us to publish aggregate numbers of national security requests, including Fisa disclosures, separately," the company said in a statement.

Apple, Facebook, Microsoft and Yahoo, the other major tech firms named in the Prism documents, have all called for greater disclosure about government requests for information. They have also strongly denied that they allow the government "direct" access to their servers, denials first reported by The Guardian when the story broke.

"Google's reputation and business has been harmed by the false and misleading reports in the media, and Google's users are concerned by the allegations. Google must respond with more than generalities. Moreover, these matters of significant weight and importance, and transparency is critical to advancing public debate in a thoughtful and democratic manner," Google said in its court filing.

Co-founder Larry Page and chief legal officer David Drummond have already called for the government to act. In a blog post the pair said the secrecy surrounding the current system "undermines the freedoms we all cherish".