The court filing in Washington came amid a firestorm of protests over revelations that the National Security Agency had accessed vast amounts of data in a surveillance program under the supervision of the special court, which operates in secret.
Google said it already publishes in its "transparency report" data on requests from law enforcement and so-called National Security Letters from the FBI.
"However, 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," a Google spokesperson said.
"Lumping national security requests together with criminal requests as some companies have been permitted to do would be a backward step for our users."
FISA refers to the Foreign Intelligence Surveillance Act, which authorized the secret court.
Google said it was seeking a court ruling to allow it to publish "limited, aggregate statistics" on orders for the company to hand over data.
(Also see: Google asks to reveal details about classified requests)
"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," the petition said.
The company said it was asking the court to affirm its "right" under the First Amendment of the US Constitution to publish the information.
Google's legal move came as the nonprofit Electronic Frontier Foundation (EFF) ramped up a campaign to pressure Congress to put an end to online snooping and come clean about what has been done to date.
More than 215,000 signatures have been logged in support of a petition at a stopwatching.us website launched last week by the EFF.
"This type of blanket data collection by the government strikes at bedrock American values of freedom and privacy," the petition contends, arguing that dragnet online surveillance violates Constitutional protections.
"We are calling on Congress to take immediate action to halt this surveillance and provide a full public accounting of the NSA's and the FBI's data collection programs."
The EFF on Tuesday teamed with Fight for the Future to launch CallDay.org website and provide a telephone number that automatically routes callers to US legislators.
"We're asking everyone concerned about their privacy to call Congress today and throughout the rest of the week," the EFF said in a message at its website.
Apple, Facebook, Microsoft and several other top Internet and technology companies have come under heightened scrutiny since word leaked of a vast, covert Internet surveillance program US authorities insist targets only foreign terror suspects and has helped thwart attacks.
Google chief Larry Page and Facebook co-founder Mark Zuckerberg have publicly condemned online spying and called for governments to be more revealing about snooping on the Internet.
"We understand that the US and other governments need to take action to protect their citizens' safety including sometimes by using surveillance," Google chief and co-founder Larry Page said in a blog post.
"But the level of secrecy around the current legal procedures undermines the freedoms we all cherish."
Google, Facebook and other technology firms have vehemently denied that they knowingly took part in a secret program called PRISM that gave the National Security Agency (NSA) and the FBI backdoors into servers.
The program was reportedly set up in 2007 and has grown to become the most prolific contributor to President Barack Obama's Daily Brief, the US leader's top-secret daily intelligence briefing.
Some of the biggest firms in Silicon Valley were involved in the program, including Apple, AOL, Facebook, Google, Microsoft, PalTalk, Skype, Yahoo and YouTube, reports said.
Internet titans contacted by AFP denied providing intelligence agencies with backdoors to networks and held firm that they only cooperated with legal "frontdoor" requests for information.
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