A former headmaster at one of Australia's most prestigious private schools on Tuesday apologised after revelations that boys were groomed for sex by paedophile teachers while he was in charge.

Knox Grammar in Sydney, whose ex-pupils include the late former prime minister Gough Whitlam and Hollywood star Hugh Jackman, has been the focus in recent days of a national enquiry into institutional responses to child abuse.

The royal commission has heard disturbing claims of abuse at Knox which allegedly happened between the 1970s and 2012, with one ex-student saying the school harboured "a large paedophile cohort".

Ian Paterson was the principal for 30 years until 1998 and it is alleged that he failed to tell police about incidents of abuse and provided references for teachers later charged with sex offences.

In a witness statement to the commission, Paterson admitted he made mistakes and said he was sorry for the pain inflicted on boys under his care at the day and boarding school.

"I should have known and I should have stopped the events that led to the abuse and its tragic consequences for these boys in my care and their families," he said.

"My abject failure to provide for you a safe and secure place at Knox strikes at the very heart of a responsibility of a headmaster.

"I commend your courage in coming forward," he added, referring to pupils who said they were abused.

"Knowing that I was your headmaster when much of this abuse occurred is devastating."

Paterson has not been implicated in the abuse of boys under investigation, but the commission on Monday heard evidence that he inappropriately touched a girl on stage during rehearsals for a musical with another school in 1989.

His statement came before he is due to give evidence about his knowledge and management of teachers accused of abusing children while he was in charge.

Australia opened the Royal Commission into Institutional Responses to Child Sexual Abuse in April 2013, after more than a decade of pressure to investigate claims of paedophilia in religious organisations, schools and state care.

The commission's hearings have covered damaging allegations of child abuse involving places of worship, orphanages, community groups and schools dating back decades.

In September last year, it was extended by a further two years to deal with the thousands of victims who have come forward.