NSA / Reuters The National Security Agency headquarters in Fort Meade, Md.

The largest Internet companies in the United States are turning up the pressure on the federal government in their quest to publish more information about their role in the National Security Agency’s controversial surveillance programs. In simultaneous petitions filed Monday with the Foreign Intelligence Surveillance Court (FISC), Google, Yahoo, Facebook and Microsoft demanded permission to be more transparent about the data requests they receive from the feds. Monday’s court fillings represent the latest attempt by the Internet giants to demonstrate their independence from the government’s vast snooping operation. Once again, the nation’s largest phone companies, including AT&T and Verizon Wireless, are absent from the push for greater transparency.

As blockbuster revelations about the NSA’s surveillance programs continue to be published — thanks to documents leaked by former NSA contractor Edward Snowden — the Silicon Valley giants have come under intense scrutiny about the extent of their participation in the programs. For nearly three months, the companies have been trying to push back against the notion that they allow the government unfettered or “direct” access to user data as part of a U.S. intelligence system called PRISM, which was revealed in June.

The NSA uses the PRISM system to examine data — including e-mails, videos and online chats — that it obtains from the companies under Section 702 of the 2008 Foreign Intelligence Surveillance Act (FISA) Amendments Act. The tech giants are prohibited from revealing anything about the requests they receive for such information, because FISA requests are classified top-secret, and the companies are barred from even discussing them. Two weeks ago, Director of National Intelligence James Clapper announced plans for the government to issue its own annual “transparency report” with limited information about the number of national security orders made to the companies. The Internet giants say Clapper’s initiative, while laudable, doesn’t go far enough in the interest of transparency.

(MORE: AT&T and Verizon Stay Silent About NSA Internet Snooping)

In June, Facebook, Microsoft, Apple and Yahoo reached an agreement with the government to release aggregate numbers of total U.S. data requests, but the companies were not permitted to break out the number of FISA requests separately. Google called the deal a step backward for transparency. In recent weeks, Google, Microsoft and Yahoo tried to negotiate with the government for permission to be more specific about U.S. intelligence requests, but those talks ended in failure, prompting the companies to take their case directly to the secretive FISA court, which is made up of 11 federal judges appointed by U.S. Chief Justice John Roberts.

In its motion on Monday, Google asked for permission to publish detailed statistics about the types of national security requests it receives under FISA. The company also asked the court to hold an open hearing, rather than the secret proceedings that are the FISA court’s standard practice. Also on Monday, Google and other tech companies met with President Obama’s Review Group on Intelligence and Communications Technology, which is tasked with examining the balance between national security and civil liberties.

In a company blog post, two Google officials, Richard Salgado, Director, Law Enforcement & Information Security and Pablo Chavez, Director, Public Policy and Government Affairs, outlined the message the company planned to convey to the Review Group: “The levels of secrecy that have built up around national security requests undermine the basic freedoms that are at the heart of a democratic society.”

(MORE: Apple, Google, Facebook Join Civil Liberties Groups for NSA Transparency Push)

Yahoo general counsel Ron Bell argued in a blog post that the secrecy surrounding the government’s surveillance programs undermines public trust in the Internet giants. “We believe that the U.S. Government’s important responsibility to protect public safety can be carried out without precluding Internet companies from sharing the number of national security requests they may receive,” Bell wrote. “Ultimately, withholding such information breeds mistrust and suspicion — both of the United States and of companies that must comply with government legal directives.” Bell added: “The United States should lead the world when it comes to transparency, accountability, and respect of civil liberties and human rights.”

Colin Stretch, Facebook’s general counsel, wrote in a blog post that the U.S. government needs to go further in assuaging the fear and mistrust that have arisen from the flood of NSA surveillance disclosures. “The actions and statements of the U.S. government have not adequately addressed the concerns of people around the world about whether their information is safe and secure with Internet companies,” Stretch wrote. “We believe there is more information that the public deserves to know, and that would help foster an informed debate about whether government security programs adequately balance privacy interests when attempting to keep the public safe.”

Civil liberties groups praised the Internet giants’ push for greater transparency. Kevin Bankston, Free Expression Director at the Center for Democracy and Technology, said in a statement that it’s important that Internet companies be allowed to publish the number of specific types of FISA requests that each company receives. In July, Bankston’s group sent a letter to the White House and Congress calling for more transparency.

“Our joint letter was addressed to the Obama Administration and to Congress, and our coalition of Internet companies and free speech advocates will continue to press those branches of government for action around transparency reporting,” Bankston said. “However, today’s filings open a third major front in the battle for surveillance transparency, and we look forward to supporting these Internet companies as they push for the right to be more open with their users about what they do—and don’t do—when the government asks for their users’ data.”