Veteran journalist Vincent Browne has offered to step aside as moderator in a live TV debate on the referendum to encourage the Taoiseach to take part.
With just three weeks until polling day, Enda Kenny ruled out appearing on the TV3 programme to go head-to-head with Sinn Fein leader Gerry Adams given the broadcaster's involvement.
"I do not understand what his objections are but nonetheless, I do not wish to inhibit this important public debate from proceeding," said Mr Browne. "The public's right to information far outweighs any other issues which may act as a barrier to a substantial debate on an issue of national and vital importance."
A spokesman for the Taoiseach said he had received a formal written invitation from TV3 and that he would take it into consideration. Mr Kenny previously declined to attend a debate for political party leaders on the channel in the run-up to the general election of 2011.
This came after Mr Browne was forced to apologise the previous year for remarking that the Fine Gael leader should go into a dark room with a revolver and a bottle of whiskey. Fine Gael lodged an official complaint with the Broadcasting Authority of Ireland about the remark.
TV3 has now called for a different journalist to moderate the debate, should it go ahead on May 29, with director of news Andrew Hanlon stating the channel would do its best to deliver balanced and fair news.
"TV3 has done its utmost to facilitate a debate between the Taoiseach and Sinn Fein leader in order to help our viewers make an informed decision on the forthcoming referendum, the outcome of which will be crucial to the future of this country," said Mr Hanlon.
Earlier, Sinn Fein argued that the Taoiseach was running scared after refusing to take part in the debate.
Pearse Doherty said he had a duty to the public to argue his case for a Yes vote in the referendum and that he should put aside his "petty differences" with the presenter.
Neither the Taoiseach nor Mr Adams have yet taken part in a televised discussion on whether Ireland should vote to adopt the stability treaty on May 31.