Two Democratic senators warned Friday that a new report detailing thousands of instances in which the National Security Agency broke laws while spying was only “the tip of a larger iceberg” of surveillance violations.

“We have previously said that the violations of these laws and rules were more serious than had been acknowledged, and we believe Americans should know that this confirmation is just the tip of a larger iceberg,” said Sens. Ron Wyden, D-Ore., and Mark Udall, D-Colo., in a prepared statement.

The senators’ comments follow a Washington Post report Friday that detailed the NSA breaking privacy rules or overstepping its legal authority thousands of times each year since Congress granted the agency broad new powers in 2008.

Wyden and Udall said that while Senate rules prohibit them confirming or denying some of the details in media reports, “the American people have a right to know more details about of these violations.”

“We hope that the executive branch will take steps to publicly provide more information as part of the honest, public debate of surveillance authorities that the administration has said it is interested in having,” they said.

To help curb future surveillance violations, the senators said a “robust and well-staffed public advocate” is needed for the Foreign Intelligence Surveillance Court, often called the FISA Court, which oversees requests by federal law enforcement agencies for surveillance warrants against suspected foreign spies inside the U.S.

“Without such an advocate on the court, and without greater transparency regarding the court’s rulings, the checks and balances on executive branch authority enshrined in the Constitution cannot be adequately upheld,” the senators said.

Earlier Friday, House Minority Leader Nancy Pelosi, D-Calif., said the latest reports of NSA privacy violations were “extremely disturbing.” But she stopped short of calling for reforms of the nation’s spying laws, saying “current laws governing NSA’s collection activities contain safeguards to ensure the protection of privacy and civil liberties.”

“Congress must conduct rigorous oversight to ensure that all incidents of non-compliance are reported to the oversight committees and the FISA Court in a timely and comprehensive manner, and that appropriate steps are taken to ensure violations are not repeated,” she said.