The Health Minister Leo Varadkar says he does not see a reason why Enda Kenny would agree to debate Micheál Martin, who he described as "the leader of a third party".
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Mr Martin was the target of criticism a number of times at Fine Gael's party conference over the weekend.
Minister Varadkar says there would be no point in a TV debate between the Taoiseach and Fianna Fáil leader.
He said: "I don't really think there is a point, you know Fianna Fáil is a third party.
"It was a third party in the last General Election, it'll almost certainly be the third party in the next, and it is in the polls at the moment.
"So, I don’t see why Enda Kenny would go head-to-head with the leader of a third party."