Mr Adams was speaking in the Irish parliament where the case of Belfast woman Maíria Cahill was discussed.
Irish Prime Minister Enda Kenny described Ms Cahill as "a force to be reckoned with".
Mr Adams said the IRA had sought to deal with some cases of abuse when asked to do so by families and victims.
"While the IRA volunteers were acting, in my opinion, in good faith, the IRA was ill-equipped to deal with such matters," he said.
"IRA actions against such sex offenders failed victims and that is a matter for profound regret from me and other republicans.
"So I'm acutely conscious that there may be victims who were let down or failed by the IRA's inability to resolve these cases.
"I want to apologise to those victims. Those who wish should come forward now and report their complaints to the appropriate authorities. "
|Gerry Adams apologizing to sex assault victims mistreated by the IRA|
He said Ms Cahill's story involved the leadership of the IRA.
"The most powerful people in the IRA conspired in this and I think it is reprehensible that a young woman of this courage and bravery should be kicked about in the last week," he said.
He said a number of other alleged victims of IRA abuse had contacted Ms Cahill with their stories.
Mr Kenny compared the IRA's handling of abuse cases and moving suspected abusers to other jurisdictions with past practice in the Catholic Church.
"These very much mirrored in what has happened here with IRA sexual abusers," he said.
He challenged Mr Adams to reveal if IRA members who were believed to have carried out abuse were exiled to the Republic of Ireland.
"Are those people still here? Is this true? Do you know of any activities they are involved in now?" he said.
"These are the most serious matters for everybody. Sexual abuse was rampant in many sectors in Irish society, not alone in paramilitary organisations, but you have responsibility for this, but we need to know."
|Maíria Cahill met with Irish Prime Minister Enda Kenny on Wednesday|
He called her, 'A force to be reckoned with'
Charges were dropped against those said to have been involved in the IRA inquiry and the alleged rapist was acquitted.
Earlier this month, the Belfast woman waived her right to anonymity to speak to BBC Northern Ireland's Spotlight programme.
She said that in 1997, when she was 16, she was subjected to a 12-month cycle of sexual abuse, including rape, by a man who was believed to be a member of the IRA.
Ms Cahill described how the IRA questioned her repeatedly, often several nights a week, for months about the abuse allegations, before summoning her to a meeting with her alleged abuser in early 2000.
Ms Cahill later went to the police, and a case was brought against Martin Morris.
All charges were dropped and Mr Morris was acquitted after Ms Cahill withdrew her evidence.
I'm sure there is a story there! It's curious why Ms Cahill met with the Irish PM and Gerry Adams apologized in the Irish parliament, when the abuse occurred in Northern Ireland.
Anyway, Mairia Cahill is my hero for the week. God bless her in her attempts to get justice for herself and other girls/women who were sorely abused in 'the troubles'.