Lawmakers from both parties expressed frustration Monday that the FBI did not inform them that it was conducting an investigation that included former CIA Director David H. Petraeus. But it’s not at all clear that the agency violated protocol — or the law — in keeping the inquiry to itself.

The FBI has long followed a Justice Department policy that bans the agency from discussing ongoing criminal investigations with the legislative branch and others. In the case of Petraeus, who resigned Nov. 9 after admitting to an extramarital affair, the FBI’s inquiry began as just that: a criminal investigation into harassing emails sent by Petraeus’ mistress and biographer, Paula Broadwell.

“The bottom line is that a criminal investigation is not something that would normally be subject to disclosure,” said William E. Moschella, a former counsel to the House Judiciary Committee and assistant attorney general in the Justice Department. “This one just happens to have a significant intel overtone to it.”

A senior Democratic aide said that the FBI, upon learning of Petraeus’ involvement with Broadwell, probably designated the case as a “sensitive investigative matter,” a form of inquiry that requires top FBI and department officials to be informed but would not necessarily involve communication with members of Congress.

“A lot of the carping I’ve heard coming from some members on this is kind of ridiculous,” the aide said. “Anyone who’s dealt with the FBI knows this is how the bureau approaches these things.”

Many in Congress, however, are more concerned with the national security implications of the Petraeus case than with the procedures used by the FBI and Justice Department in more traditional law enforcement cases.

Lawmakers, including Senate Intelligence Chairwoman Dianne Feinstein, D-Calif., believe that federal law is on their side. They cite a broadly written provision in a 1947 national security law that compels the executive branch to keep congressional panels “fully and currently informed” about U.S. intelligence activities.

The circumstances surrounding Petraeus’ affair may rise to that level, according to Jack Goldsmith, a Harvard law professor and former assistant attorney general in the Justice Department.

“The FBI investigation might have been primarily a law enforcement matter until very recently — though it seems like any investigation into security breaches of the CIA director’s computer system or communications by definition implicates counterintelligence,” Goldsmith wrote on a legal blog on Nov. 10, though he stressed that more details about the investigation are still needed.

The chairmen and ranking members of the House and Senate Intelligence panels receive quarterly, top-secret briefings on counterintelligence activities, but it’s unclear that the Petraeus investigation ever fell into that category.

Both Democrats and Republicans have expressed fears that Petraeus’ affair may have resulted in sensitive national security information being compromised, and while the FBI found no evidence of that, some lawmakers made it clear on Monday that felt cut out and intended to ask further questions.

An aide to Sen. Charles E. Grassley, the top Republican on the Judiciary Committee, said the Iowa lawmaker is pursuing more information from the FBI. The panel has oversight authority over the bureau.

“Sen. Grassley’s staff has requested a briefing on the FBI’s role,” spokeswoman Beth Levine said. “Like many Americans, the ranking member has questions for the bureau and the Justice Department that, if the administration answers, may shed light on who knew what, when they knew it and the implications on national security.”

Feinstein repeated her promise to investigate why her committee, which oversees the CIA, was not informed about the FBI inquiry until Petraeus’ resignation.

“You cannot keep these things from the people who have responsibility for oversight,” Feinstein told MSNBC on Monday, adding that she “absolutely” should have been informed about Petraeus.

Feinstein said the chairmen and ranking members of the House and Senate Intelligence Committees are routinely briefed on “operationally sensitive matters.” She added, “This is certainly an operationally sensitive matter, but we weren’t briefed. I don’t know who made that decision.”

While key senators are seeking more information about the investigation, one of the few members of Congress who knew of the FBI investigation before Petraeus resigned — House Majority Leader Eric Cantor, R-Va. — has not made any determination about whether any reporting protocols or laws were violated by the law enforcement agency, according to a spokesman.

“We cannot speculate. We simply don’t know all the facts,” Cantor spokesman Rory Cooper said. “If there is a threat to national security or classified information, the FBI is obligated to inform Congress.”

At the very least, there are likely to be political ramifications surrounding the FBI’s conduct, particularly from Feinstein’s committee. The Senate Intelligence Committee has previously sought more accountability and communication from the FBI.

“In several instances the FBI has not kept the committee fully and currently informed of its intelligence activities, nor has it responded to congressional questions for the record in a reasonable time frame,” the committee said in a 2009 report.

Kevin Whitelaw and Rob Margetta contributed to this report.