Two US congressmen introduced a bill on Thursday compelling the Obama administration to declassify the secret legal justifications for the wide-ranging surveillance programs run by the National Security Agency.

The disclosure bill, a complement to one pushed in the Senate last week, is the latest in a series of legislative attempts to rein in the NSA's collection and analysis of Americans' phone records and, potentially, Internet usage.

The bill is also another sign that civil libertarian factions of both political parties are uniting in the wake of surveillance disclosures published this month in the Guardian and the Washington Post. Its sponsors are Adam Schiff, a California Democrat, and Todd Rokita, an Indiana Republican.

Schiff and Rokita's bill instructs attorney general Eric Holder to declassify opinions of the secret Foreign Intelligence Surveillance court, known as the Fisa court, that explain the government's authorities – and restrictions – for collecting the phone records of millions of Americans, its rules for searching through them, and the boundaries of an Internet communications harvesting program, known as Prism, that the Obama administration says focuses on foreigners.

The bill would "increase the transparency of the Fisa court and the state of the law in this area," Schiff told the Guardian on Thursday. "It would give the public a better understanding of the safeguards, as well as the scope of these programs."

"In order to have an informed public debate on the merits of these programs, it is important for the American people to know how such programs have been authorized, their limits and their scope," Schiff said in releasing the bill.

"This legislation affirms that Americans have a right to know the assumptions and legal interpretations that are guiding our national security decisions," Rokita said. "Just as importantly, it provides that information to the public in a way that does not compromise specific security techniques. Our bill will help Congress and the American people exercise proper oversight, while still enabling us to do everything possible within the bounds of the constitution to protect ourselves from those who would harm us."

The Obama administration has justified the surveillance programs using aspects of two laws: section 215 of the 2001 Patriot Act, the so-called "business records" provision; and section 702 of the 2008 Fisa Amendments Act. But a handful of US senators, especially Ron Wyden, Democrat of Oregon, and Mark Udall, Democrat of Colorado, of the intelligence committee, have warned for years that the government's secret interpretations of those provisions authorizes far more surveillance on Americans' communications than legislators intended.

It is those interpretations, which Wyden and Udall have taken to calling "secret law", that Schiff and Rokita seek to disclose. Schiff said it is difficult for Americans to express their preferences for "the balance between privacy and security without these opinions being public".

During a House intelligence committee hearing on Tuesday, representatives of the NSA, the Justice Department, the Director of National Intelligence and the FBI indicated that they were willing to declassify the secret court's rulings, provided they could figure out a way to exclude references to classified information while making the public version of the rulings comprehensible. They did not give a timeline for their efforts.

In March, the presiding judge of the Fisa court, Reggie Walton, wrote to Wyden and Udall to inform them that he "would not anticipate" releasing many of the court's opinions, given their "fact-intensive nature".

The disclosure bill complements a bipartisan bill entered in the Senate on 11 June, sponsored by eight senators, to compel release of the surveillance court's secret rulings.

It also follows a more expansive effort in both chambers of Congress to actively restrict the amount of Americans phone records that the NSA can collect and analyze. Wyden and Udall have introduced a bill that would require intelligence agencies to demonstrate a "link to terrorism or espionage" before collecting any American's phone data. On Tuesday, three congressmen, Republican Justin Amash of Michigan and Democrats John Conyers of Michigan and Jared Polis of Colorado, introduced a complementary bill that would restrict the NSA's ability to collect phone data on any American unconnected to an ongoing investigation.

Neither bill, nor any other introduced in Congress thus far, would restrict the collection of foreigners' online communications under the NSA's Prism program. That program, the Obama administration says, does not target Americans, but the administration has been less clear about whether and how much Americans' online communications are inadvertently swept up by Prism.

Currently, the intelligence agencies and the Obama administration say that Americans' privacy is protected because the NSA needs "reasonable, articulable suspicion" of a link to terrorism or foreign espionage before it sifts through its phone records database. But Deputy Attorney General James Cole told the House intelligence committee on Tuesday that the NSA determines for itself whether that standard is met. Civil libertarians have also pointed out that the language of section 215 of the Patriot Act governs the collection of data, not its analysis.