Adams accused Taoiseach of making 'sliabheen' remarks over Mairia Cahill
Mr Kenny will refer the case of Ms Cahill's rape to the Oireachtas justice committee for examination.
The Taoiseach told Mr Adams if the allegations were being made about Fine Gael, he "wouldn't last five minutes".
"Not five minutes," he said.
"You attended and spoke to this young woman. And she says you weren't speaking about the weather," he added.
Mr Kenny said the "false assumption of a war being waged" did not justify abductions, shootings or kangaroo courts.
He is due to meet with Ms Cahill in Government Buildings tomorrow.
The Taoiseach also targeted Sinn Fein vice-president Mary-Lou McDonald for criticism.
"You can't have blind allegiance from your deputy leader," he said.
Mr Adams accused Mr Kenny and Fianna Fail leader Micheal Martin of "playing politics" with the issue and denied the allegations.
Speaking following his heated Dail exchanges, Mr Adams also accused Mr Kenny of making “sliabheen” remarks.
“I think the Taoiseach’s comments were entirely reprehensible. I made that clear. The way that he and the leader of Fianna Fail have dealt with this very, very sensitive issue has been to politicise it,” he said ahead of an event at Liberty Hall.
“The assertion, allegation, the accusation that Sinn Fein has been engaged in a cover-up, that’s totally and absolutely untrue. That I have been engaged in a cover-up, that’s totally and absolutely untrue.
“The issue of abuse of any kind is the most heinous kind, most particularly child abuse. Anybody who has any information on this, including the Taoiseach and the leader of Fianna Fail should bring it to the appropriate authorities.”
Mr Adams refused to say whether he believed he has been damaged by Ms Cahill’s allegations.
“The electorate will have the opportunity to judge this and many other issues,” he said.
He added that he would be willing to meet Ms Cahill if she requests to do so.
“We were in touch with her. I am quite prepared, the party is quite prepared, and that’s a matter we can work out with her if she wants to meet with us. I’ll meet with anyone.”