The police failed, according to a report, to three women who said they had been sexually abused by an older member of the IRA when they were teenagers.
Máiría Cahill, a member of a prominent Republican family, told police in 2010 that she had been raped.
Two other women said they were abused by the same man.
PSNI Chief Constable George Hamilton apologized "unequivocally for the injury and distress" inflicted on women.
He added that the PSNI investigation was "very much under the high expectations that I and my officers set ourselves and the public expects."
Three PSNI officers were disciplined on the findings of the police ombudsman.
A fourth officer, who would have been subject to disciplinary action, has retired.
The police ombudsman said the PSNI had failed women "in a number of key areas".
Dr. Michael Maguire also said that prior to the founding of PSNI in 2001, RUC Northern Ireland's police received information about allegations of child abuse by an IRA member 10 years before filing the complaint, but had not acted.
He noted, however, that the inability of the police to investigate was based on a desire to protect informants within the IRA.
The police have described the abuses as "scandalous". Mária Cahill has asked PSNI police chief George Hamilton to apologize and "urgently" meet her to discuss the case.
Ms. Cahill told police that she had been tortured and raped between 1997 and 1998 by an alleged IRA member named Martin Morris.
Her great-uncle Joe Cahill was one of the founders of the Provisional IRA.
She told BBC Northern Ireland's Spotlight Program in October 2014 that the IRA had interrogated and covered her repeatedly about the allegations.
Martin Morris, who is believed to live in London, has always rejected the allegations and was acquitted of rape and IRA membership charges when his trial collapsed in 2014.
Four other alleged IRA members alleged to have been interrogated, Ms Cahill, were also acquitted of all charges.
The process collapsed when the women withdrew their evidence and said they had lost faith in the criminal justice system.
The three women later received an apology from the prosecution after an independent review had strongly criticized how the case was handled.
The police ombudsman said they had failed by the police.
Dr. Michael Maguire described the PSNI investigation as "disjoint" and "inconsistent".
He criticized a decision to divide the investigation into two units, one with expertise in terrorist cases and another specializing in dealing with victims of sexual violence.
But he dismissed allegations that "someone was protected from prosecution" or that the investigation was "subject to adverse political interference".
The Ombudsman also criticizes the RUC, the predecessor of the PSNI.
Dr. Maguire said his investigators found that in 2000, the RUC received information linking a man to the alleged abuse of children and that the IRA investigated the allegations.
"However, when the RUC received this information, it was not disseminated and there is no evidence of police investigation or investigation as a result," he said in a statement.
"The material was sufficiently specific that the police themselves had made superficial investigations identifying potential victims of abuse."
Mária Cahill said she was confirmed by the results and apologized.
"I have been very disappointed with both aspects of the criminal justice system, both the PPS and the police regarding this situation," she told the BBC.
"I do not think there are excuses that can be given at this stage.
"I'll never get a court conviction for what happened to me, but I think lessons have to be learned absolutely and I call on the chief of police to apologize."
PSNI chief of police George Hamilton gave Mrs. Cahill and the other two women a "clear" apology.
He added that the Ombudsman of the Police is "an essential part of the mechanisms by which we can be held accountable".
He said the report found "failures by the RUC in 2002 to share important information linking a man to the alleged abuse of children" and that he "noted other errors in PSNI investigations".
"These standards do not meet the high expectations that I and my officers set ourselves and expect the public.
"I accept the report and since then we have implemented all the recommendations of the PONI (Police Ombudsman Northern Ireland) for changes in the PSNI policy."
He added that "many changes have been made to the PSNI since the report was produced," including the launch of its own public safety department in 2015.
"A vehement apology"
Mária Cahill has also called on the President of Sinn Féin, Mary Lou McDonald, to apologize for the role of the party in a cover-up.
In a letter outlining his findings, the Ombudsman said the police had news that Martin Morris was suspended by Sinn Féin in 2000, three years after the party learned of the alleged abuse.
"Sinn Féin has repeatedly insulted me over the media over the last four years, saying that they are not involved in a cover-up of abuse," Mária Cahill told the BBC.
"I told Senior Sinn Féin members about my abuses in 1997 and 1998.
"One of them was then Advisor to Gerry Adams and the other later politician, a very senior politician.
"They had information that he was also suspected of abusing others."
She added: "No one in Sinn Féin has suspended this man until 2000. So there is a period of three years when Sinn Féin was content to have a child molester with access to children in his ranks.
"I think the party really has to say today, yes, it has told the truth.
"It's very hard to hear how Sinn Féin questions my credibility, and I think Mary Lou McDonald owes me a heavy apology."