Speaking at his party's presidential dinner, Mr Kenny said that from materials and documents he had read, it was his opinion that Mr Adams was not only an IRA member but also a senior figure on its army council.
"From all the evidence I have read and from all the evidence I have heard, I believe Gerry Adams was a member of the IRA and I was led to believe he was also a member of the army council," he said.
Mr Kenny said that Mr Adams's calls for a truth commission in the North would count for nothing unless he was honest about his role during the Troubles, which claimed more than 3,000 lives.
"When Deputy Adams says to me he wants a truth and reconciliation commission, I'd like him to be absolutely truthful about this" he said.
He also contrasted Mr Adams's continual denial of being in the IRA with the admission by Martin McGuinness about his senior role in the paramilitary organisation.
"I had a serious discussion with Martin McGuinness, Deputy First Minister of Northern Ireland, and he was forthright enough and honest enough to say he was a member of the IRA. So Gerry Adams might like to make a statement about that."
Given the gravity of his words, Mr Kenny was asked to clarify his comments and whether he held Mr Adams responsible for murder.
He replied: "I was asked a question, do I believe Gerry Adams was a member of the IRA and I said, the evidence I have read and heard led me to believe he was and was a member of the army council -- and he might like to make a statement on that," he responded.
Mr Kenny was speaking one week after Dolours Price accused Mr Adams of involvement in terrorist activity in a newspaper interview.
Price, who, along with her sister Marian, was jailed for her part in the Old Bailey bombing, accused Mr Adams of personally ordering the abduction of people who the IRA considered to be traitors.
Price is utterly opposed to the peace process and unrepentant about her IRA role.
She also admits that her campaign against Mr Adams is in response to his involvement in the peace process.
"Dolours Price is not very friendly towards Sinn Fein these days, she is an anti-peace process republican" a spokesman for Sinn Fein said in response to her allegations.