WASHINGTON — A Justice Department investigation has found that FBI agents, including several supervisors, cheated on an important test covering the bureau’s policies for conducting surveillance on Americans.

Justice Department Inspector General Glenn Fine said Monday that his limited review of allegations that agents improperly took the open-book test together or had access to an answer sheet has turned up “significant abuses and cheating.”

Fine called on the FBI to discipline the agents, throw out the results and come up with a new test to see if agents understand new rules allowing them to conduct surveillance and open files on Americans without evidence of criminal wrongdoing.

FBI Director Robert Mueller said that in cases in which misconduct has been determined, personnel actions were taken, and that process continues.

“We will follow up in each of the 22 cases the IG has found for disciplinary action, as appropriate, as well as any other allegations of misconduct,” the FBI director said in a statement.

The review of the exam on surveillance rules follows Fine’s report last week on the FBI’s scrutiny of domestic activist groups. That investigation found that the FBI gave inaccurate information to Congress when it claimed a possible terrorism link to justify monitoring an anti-war rally in Pittsburgh in 2002.

In the inquiry into the exam, the inspector general looked only at four FBI field offices and found enough troubling information to warrant a comprehensive review by the FBI.

In one FBI field office, four agents exploited a computer software flaw “to reveal the answers to the questions as they were taking the exam,” Fine said.

Other test-takers used or circulated materials that essentially provided the test answers, he said.