Mr Kenny made the dramatic statement about the Sinn Féin leader on Saturday night while attending a party dinner in Dublin.
The Taoiseach said he had seen documentary evidence which left him in no doubt that Mr Adams was not only a member of the IRA but had been a senior figure on its army council.
The unprecedented statement by Mr Kenny about an opposition member in the current Dáil was prompted after claims last week by a former IRA bomber.
Dolours Price said in a newspaper interview that Mr Adams had been involved in terrorist activity. She also said he sanctioned the 1973 Old Bailey bombing, for which she was later jailed.
Mr Kenny on Saturday said that Mr Adams’s demands for a truth commission in the North could not be met unless he himself was honest about his past.
“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, when asked to clarify the remarks, reiterated his belief. He said Sinn Féin’s Martin McGuinness had been “forthright enough” to admit his own past in the IRA.
Responding to the remarks yesterday, Mr Adams said: “It is now becoming tedious that every time this Government feels under pressure it raises this issue of me being in the IRA. It is nonsense and the Taoiseach knows this.”
The Sinn Féin leader said the Taoiseach’s comments — not covered by privilege as they were made outside the Dáil — were an attempt to deflect attention from the failings in Government.
“This is another desperate and transparent attempt to deflect attention from the failures of Mr Kenny’s Government,” he said.
Mr Adams previously said legal advice suggests turning to the courts to defend his name would be “financially beyond” his means.