By Joseph Menn

SAN FRANCISCO (Reuters) - Some of the world's biggest Internet companies on Monday increased efforts to disclose more about their forced cooperation with U.S. spy agencies, and Google Inc asked a court to hold what would be unprecedented public oral arguments.

Google Inc, Facebook Inc and others met with a panel established by the White House to review the sweeping domestic surveillance exposed by Edward Snowden, a former contractor at the National Security Agency.

Separately, Google asked the secret court that approves spying requests for a public hearing on their quest to reveal how many orders the company complies with. Facebook and Yahoo Inc made their own first filings on Monday seeking the ability to disclose more about the orders following Google and Microsoft Corp filings in June.

Google's new court filing adds to its earlier petition. It complains that its reputation and business have been damaged by what it says were misleading reports that the NSA had "direct access" to its internal servers. The companies have denied those reports, and most now publish summaries that give the number of all the government requests they receive.

Most lump together foreign intelligence demands with routine criminal inquiries, though Google says it receives fewer than 1,000 National Security Letters per year, affecting fewer than 2,000 accounts.

The companies want to say more, and Google argues that its First Amendment right to speak out, especially on a matter of great political and public importance, outweighs any harm to intelligence efforts that would come from releasing more detailed but still aggregate statistics.

"The government has identified no statute or regulation that prohibits such disclosure and it is not appropriate for this court to undertake the essentially legislative function of creating such a prohibition," Google wrote in its filing with the U.S. Foreign Intelligence Surveillance Court.

The court, whose members are appointed by the U.S. Supreme Court chief justice, has never held a public session and generally hears only from the U.S. Justice Department and intelligence agency lawyers.

A Justice Department spokesman declined to comment.

Google's move follows its confirmation that it is moving more quickly to encrypt data as it moves internally at the company.

On Sunday, Brazilian television cited new Snowden documents in reporting that the NSA has tried to attack Google or at least intercept communications from its users to the company.

"As for recent reports that the U.S. government has found ways to circumvent our security systems, we have no evidence of any such thing ever occurring," a Google spokesman said Monday.

The panel established by the White House, called the Review Group on Intelligence and Communications Technology, was charged with recommending how to balance security and privacy concerns.

President Barack Obama met with the new group on August 27. On Monday, it met with the big technology companies and separately met with privacy and civil liberties groups.

Someone briefed on the first meeting said the companies were united in seeking more transparency and that they found the session "constructive."

The review panel is to provide an interim report within two months.

(Reporting by Joseph Menn; Editing by Grant McCool)