Two senators on the intelligence committee on Monday accused the National Security Agency of publicly presenting "inaccurate" information about the privacy protections on its surveillance on millions of internet communications.

However, in a demonstration of the intense secrecy surrounding NSA surveillance even after Edward Snowden's revelations, the senators claimed they could not publicly identify the allegedly misleading section or sections of a factsheet without compromising classified information.

Senators Ron Wyden (Democrat, Oregon) and Mark Udall (Democrat, Colorado) wrote to General Keith Alexander, the director of the NSA, to correct "inaccurate" portrayals about restrictions on surveillance published in a factsheet available on the NSA's homepage. The factsheet, concerning NSA's powers under Section 702 of the 2008 Fisa Amendments Act, was also supplied to members of Congress.

"We were disappointed to see that this factsheet contains an inaccurate statement about how the section 702 authority has been interpreted by the US government," Wyden and Udall wrote to Alexander, in a letter dated 24 June and acquired by the Guardian.

"In our judgment, this inaccuracy is significant, as it portrays protections for Americans' privacy as being significantly stronger than they actually are," the senators write. Yet they specified the "inaccurate" statement only in "the classified attachment to this letter", which the Guardian did not acquire.

Tom Caiazza, a spokesman for Wyden, said: "Unfortunately, we can't describe the inaccuracy in detail without divulging information that is currently classified. For now we can say that there is an inaccurate statement in the fact sheet publicly released and posted on the NSA website that portrays protections for Americans' privacy as being stronger than they are."

Many, if not most, of the items on the NSA factsheet list privacy protections for Americans' internet communications, as section 702 – the stated legal basis for the internet-based surveillance program PRISM – is supposed to concern surveillance on non-Americans outside the United States.

"This authority allows only the targeting, for foreign intelligence purposes, of communications of foreign persons who are located abroad," the factsheet reads. "The government may not target any US person anywhere in the world under this authority, nor may it target a person outside of the US if the purpose is to acquire information from a particular, known person inside the US."

It continues: "Any inadvertently acquired communication of or concerning a US person must be promptly destroyed if it is neither relevant to the authorized purpose or evidence of a crime." Targeting is "immediately terminated," the NSA states, if a foreigner enters the US or the NSA comes to believe it had mistaken a foreigner for an American – unless "that information meets specific, limited criteria approved by the Foreign Intelligence Surveillance Court", which the factsheet does not detail.

Wyden and Udall singled out that section of the factsheet for a slightly different criticism. They told Alexander they consider it "somewhat misleading", as it implies that the NSA "has the ability to determine how many American communications it has collected under section 702, or that the law does not allow the NSA to deliberately search for the records of particular Americans".

"In fact," the senators continued, "the US intelligence community has told us repeatedly that it is 'not reasonably possible to identify the number of people located inside the United States whose communications may have been reviewed under the authority' of the Fisa Amendments Act."

James Clapper. Photograph: Susan Walsh/AP

The Guardian has reported that the NSA operates a datamining program, codenamed Boundless Informant, that collates collected communications data by country of origin. The repeated assertion by US intelligence that the NSA lacks any such capability is what occasioned a March back-and-forth in the Senate between Wyden and James Clapper, the US director of national intelligence, that Clapper later conceded was the "least untruthful" he could have publicly provided.

Vanee Vines, an NSA spokeswoman, declined to comment on Monday on the Wyden-Udall letter.

Wyden and Udall are backing legislative efforts to disclose more information about how the government interprets its surveillance authorities, and also to restrict the surveillance on Americans' phone records, which depends on a different legal rationale than section 702 of the Fisa Amendments Act. Both senators have warned for years that the government secretly claimed broader surveillance powers than a plain reading of the laws permitted, but said they were barred from elaborating because of laws protecting classified information. They have also questioned the efficacy of the NSA's database of millions of Americans' phone records.

"We believe the US government should have broad authorities to investigate terrorism and espionage, and that it is possible to aggressively pursue terrorists without compromising the constitutional rights of ordinary Americans," Wyden and Udall wrote to Alexander.

"Achieving this goal depends on not just secret courts and secret congressional hearings, but on informed public debate as well."