The Police Ombudsman found the officers had failed to give information to detectives investigating the attempted murder of a colleague.
Peadar Heffron was seriously injured by a dissident republican bomb in 2010.
Repeated requests for intelligence did not get any meaningful response, the Police Ombudsman's report said.
It recommended that four intelligence officers should receive written warnings for not providing the information requested by the detectives.
However, the PSNI disagreed and imposed a lower level of sanction on two of them.
Chief Constable George Hamilton and his deputy, Drew Harris, met Policing Board members in a private session on Tuesday to discuss the report and their response.
Afterwards, Policing Board Chair Anne Connolly said there had been a "full and frank discussion" between the board and the chief constable.
"The chief constable has been asked by the board to consider if there are any further measures that now need to be taken on the back of the report, and the board has also asked its human rights adviser to conduct a review of arrangements," she said.
She said board members had sought assurances about the support being provided to Mr Heffron, "and very much welcome that he has now received an apology from the PSNI".
As captain of the PSNI's Gaelic football team and an Irish language speaker, Constable Heffron was a target for dissident republicans trying to deter Catholics from joining the Police Service of Northern Ireland.
His leg was amputated and he suffered other serious injuries after a bomb exploded under his car in Randalstown, County Antrim. He has since left the police.
Members of the Policing Board have met the chief constable over a report that called for disciplinary action against four officers.