SYDNEY — Australian Prime Minister Malcolm Turnbull will deliver a national apology to child sex abuse victims as part of the government’s response to a long-running inquiry that heard allegations against government and private institutions and prominent individuals in five years of hearings.

The apology, to be delivered on Oct. 22 after public consultations, was announced Wednesday as Turnbull outlined his government’s formal reaction to the Royal Commission into Institutional Responses to Child Sexual Abuse. Its inquiry ended in December after taking evidence from leaders such as Vatican Cardinal George Pell, who is charged with committing sex abuses himself and was accused of failing to protect children.

Turnbull’s government will adopt 104 of the 122 recommendations the royal commission made to it, including establishing a national office for child safety and joining a compensation program. The 18 other recommendations remain under consideration.

‘‘It’s been harrowing work,’’ Turnbull told a news conference in Canberra. ‘‘Now that we’ve uncovered the shocking truth, we must do everything in our power to honor the bravery of the thousands of people who came forward.’’

The royal commission, Australia’s highest form of investigation, heard more than 8,000 personal stories alleging sexual abuse. Taking evidence at 57 public hearings across the country, it heard of alleged abuse in various institutions including schools, sports and hobby groups, and religious organizations.

A counsel to the royal commission said Pell, Australia’s most senior Catholic official, and other Catholic officials had failed to exercise proper care for children.

Turnbull said the commission had revealed shocking abuse of children. ‘‘For too long the reporting of this abuse was met with indifference and denial by the very adults and institutions who were supposed to protect them,’’ Turnbull said.