Ms Cahill claims she was raped as a teenager by a suspected IRA member and said she was later interrogated by the IRA who covered up what happened.
Mr Adams said there was no doubt that Ms Cahill was caused great distress and was entitled to truth and justice.
Speaking in Belfast, he said he did all he could to support Ms Cahill and that Sinn Féin had acted in good faith.
Mr Adams, who is a member of the Irish parliament, has faced criticism in recent days by Fine Gael and Fianna Fáil.
Northern Ireland First Minister Peter Robinson has called for Mr Adams to personally apologise to Ms Cahill for how the issue was handled.
In a speech on Saturday, Mr Adams said Ms Cahill had made serious allegations about him and other Sinn Féin members.
"While I am very mindful of the trauma she has suffered, I and the others she has named reject these allegations," he said.
"These allegations have been seized upon in the most cynical, calculated and opportunistic way by our political opponents.
"Their aim has little to do with helping victims of abuse, but everything to do with furthering their own narrow political agendas."
On Tuesday, the Public Prosecution Service announced a review of three court cases linked to Ms Cahill's claims.
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.
The case of Belfast woman Maíria Cahill has been unfairly politicised, Sinn Féin president Gerry Adams has said.