The two had a twenty-minute phonecall earlier today
The Fianna Fáil leader says he will take to the Fine Gael leader next week - after the Dáil makes another attempt to elect a Taoiseach.
But Fine Gael's insisting Enda Kenny wanted to meet Micheál Martin tomorrow - after the two men spoke on the phone today.
Meanwhile Fine Gael's continuinging talks with the group of 15 Independents, while Fianna Fáil has started to speak to a number of others.
Our political correspondent, Páraic Gallagher reports from Leinster House that after being relatively silent while the talks have been ongoing Micheál Martin faced a media grilling this afternoon.
He revealed he had phoned Enda Kenny to insist the Dáil vote on a Taoiseach proceed next week, and to outline that as they were engaged in discussions with Independents they should talk again later next week:
"We agreed we wouldn't meet tomorrow, because he said he would be finishing off his discussions tomorrow, he said he was going to polish off, to use his phrase, the document."
But Fine Gael's adamant that Mr Kenny wanted to meet tomorrow and phoned and texted Mr Martin to say this but didn't get a reply back. When they do get around to talking one major hurdle could be Irish Water:
"We believe water charges should be abolished for the next five years, we're very clear on that. And as far as we're concerned, those who have paid paid, and those who haven't paid, should pay."
The group of Independents meeting Fine Gael have welcomed the contact between the two big parties - something Tipperary TD Mattie McGrath had called for earlier today:
"They have to get together and lead the country and stop their posturing because we're not going to be used as pawns in any game, and we could pull out at any time."
Ahead of Fianna Fáil meeting the group of Independents next Monday the party has also contacted others not spoken to by Fine Gael - this includes a meeting with Clare Daly and Mick Wallace this afternoon, while Galway's Catherine Connolly confirmed she'd been contacted by Fianna Fáil and was willing to listen.