Chief Constable George Hamilton said: "I met Máiría Cahill today and apologised personally to her for our failures.
"We talked about how the RUC did not investigate intelligence that they held in 2000. This intelligence linked a man to the alleged abuse of children and also stated that the IRA was investigating this.
"We also discussed how the PSNI did not effectively investigate the allegations of three victims, one of whom was Máiría, from 2010. These shortcomings contributed to a failure in the prosecution and had massive negative impact on Máiría and the other victims.
"I was struck by Máiría's courage and resilience.
“I was also struck by the fact that she shouldn't have had to display that much resilience, had Máiría and the other victims been better supported by the Police Service and by the wider criminal justice system.
“We have all failed them and for that I once more apologise. The responsibility for the failing of these cases rest with the Criminal Justice system and not with Máiría or any other victim.
"I fully accept the Ombudsman Report and we discussed how the organisation, and the criminal justice system, today is very different as a result of Máiría 's courage and strength in speaking out.
"We discussed how the Ombudsman noted that the previous intelligence failures would not occur today.
"We also discussed the improvements driven by reforms in the PPS and PSNI, with investigators and prosecutors working more closely together to better support victims. This has been enabled by the formation of PSNI's Public Protection Branch and the PPS's Serious Crime Unit.
"Máiría and I agreed that this was the first of many conversations between her and the Police Service, as we seek to learn from our mistakes.
“I am keen to meet Máiría again to ensure that we improve these critical services to benefit all victims."