Fine Gael leader Simon Harris has warned that no-one should take his party's participation in the next government for granted.
The outgoing Taoiseach was speaking after a meeting of the British-Irish Council near Edinburgh, which he had to leave early following warnings about the impact of Storm Darragh.
As speculation continues to swirl about a rotational taoiseach arrangement, he gave a frosty response to the suggestion that negotiations are simply a formality ahead of Fine Gael and Fianna Fáil going back into government together.
"There is far too much presumption in relation to the outcome of government talks before government talks have even taken place," he said.
"I wouldn’t take my party for granted and I think fewer public musings and more concrete engagement is the way to proceed."
Simon Harris had a place at the top table for the press conference after the summit, but his name and seat were removed when he opted to go to the airport earlier than planned.
Micheál Martin had already left the conference venue, also citing the weather.
Earlier, Northern Ireland’s First Minister and Sinn Fein’s deputy leader Michelle O’Neill had pointed an accusing finger at the Fianna Fáil leader for encouraging co-operation between political rivals north of the border but refusing to even speak to her party about government formation.
"I think the thing that’s not lost on me is the irony of Micheál Martin’s approach," she said.
"This is a man who comes to Belfast regularly and talks about partnership and inclusivity and respect and parity of esteem, but that does not apply to our party, so I think that irony will not be lost on the voters either."
No left bloc, Regional Independents open
Today, following a meeting between the two parties, the Social Democrats rejected Labour's suggestion of forming a left-wing negotiating bloc.
Social Democrats deputy leader Cian O'Callaghan said his party would "go it alone" and would meet Fianna Fáil and Fine Gael next week for preliminary talks.
Labour will hold an internal meeting tomorrow to decide its next steps.
Party leader Ivana Bacik repeated that she remains committed to the goal of forming a common platform with other left parties.
The Regional Group of eight independents said this evening that it "is willing to engage if and when we get an invitation" to discuss government formation, but stipulated that it "would be desirable that Fianna Fáil and Fine Gael first have agreement on the rotating taoiseach".
"In the event of an invitation the group will meet to discuss strategy and appoint our negotiators," a statement read.
"We would enter talks on the basis that we would be part of government," and any "programme for government would have to reflect" the group's "concerns and initiatives".
Meanwhile, Green party leader Roderic O'Gorman insisted that he would not go into government and would instead concentrate on rebuilding his party following it's electoral drubbing.
"The prospect of the Green Party being part of the next government is very unlikely. We haven't received a mandate from the people to go back into government."
Speaking after a meeting in Dublin of European Greens, Mr O'Gorman urged progressive parties to seriously engage in government negotiations.
"The only way progressive policies get implemented is by parties taking that risk."
He said that Ireland faced a "fork in the road" as right-leaning independents would have a very different approach on a whole range of issues, not just climate.
'Not presuming anything' - Martin
Asked if it could be taken for granted that Simon Harris would be once again be taoiseach as part of a rotational agreement, Micheál Martin replied that nothing could be taken for granted.
"I think we have to respect every party and I think until we get into substantive talks, I'm not presuming anything," he said.
"We have sounded out a number of independents this week, I'm due to meet with the other political parties next week, so I think, in earnest, there will be meetings next week.
"I take nothing for granted, and until agreements have been reached and completed, nobody can take anything for granted."
Sinn Féin leader Mary Lou McDonald said she believed another Fine Gael and Fianna Fáil coalition would be bad for the country.
Ms McDonald told her party's supporters last night that their TDs, Senators and MEPs were not giving up on their objectives and they should retain a sense of hope.
Meanwhile, in the aftermath of losing 11 of its 12 Dáil seats, the Green Party is hosting an annual congress of European Greens in Dublin on the theme of shaping the fight for democracy and nature.
Elsewhere, Kerry independent TD Michael Healy-Rae has confirmed he met Micheál Martin on Wednesday. No commitments were given but they will talk again Mr Healy-Rae said.
Additional reporting by Sandra Hurley
