Sen. Ron Wyden, D-Ore., agreed, saying the incidents seem to point to a broader problem.
"The Government Accountability Office has been warning about this problem for a decade. And it seems to me in this administration, there's been pretty much a culture of disregard for privacy, and that's part of the problem," he said.
Both senators spoke on CNN's "Late Edition."
Last week, Secretary of State Condoleezza Rice apologized to presidential candidates Hillary Rodham Clinton, John McCain and Barack Obama after the department confirmed the passport files had been compromised. It was not clear whether the workers - two have been fired - saw anything other than the basic personal data - such as name, citizenship, age, Social Security number and place of birth - that is required when applying for a passport.
The State Department's inspector general is investigating.
Attorney General Michael Mukasey has indicated that prosecutors would likely wait until the inspector general concludes that inquiry before deciding whether to open an investigation of its own.
On Sunday, Specter urged Mukasey to take up the case, saying the breach could be a violation of several federal criminal statutes. Specter also indicated that the Judiciary Committee might take a look as well.
"I think privacy is a very fundamental matter. And if you can't have privacy for Senator McCain and Senator Clinton and Senator Obama, so what's the average person facing?" Specter said. "It ought to be pursued very diligently, in a tough way."
The two companies that provided the workers for the State Department - Stanley Inc., of Arlington, Va., and The Analysis Corp., or TAC, of McLean, Va. - have said their employees' actions were unauthorized and not consistent with company policies.
