Leo Varadkar and Micheál Martin will meet today for “exploratory talks” on Government formation.

It may mark the first step towards a grand coalition between Fine Gael and Fianna Fáil.

Meanwhile, the Sinn Féin leader Mary Lou McDonald addressed almost 1,000 people at a Sinn Féin rally in Cork last night.

The party is holding the second in a series of rallies in Dublin this evening.

Deputy McDonald said the rallies, which will also be held in Cork, Newry, Cavan and Galway were an attempt to bring the conversation about a Government for Change to the people.

She rejected Leo Varadkar’s claim that the events were an example of a “campaign of intimidation and bullying.”

“Rather than being offensive or worse being abusive towards those of us that have a mandate for change, I think now is the time for big ideas and for working together,” she said.

“It was a huge meeting; it was absolutely packed. I suspect that will be the case right across the country.”

Mr Varadkar said his talks with Deputy Martin were just exploratory and said he would discuss the outcome with his party before making any decisions.

On Newstalk Breakfast, Fianna Fáil TD Anne Rabbitte, who is a member of her party’s negotiating team, said she was optimistic a second election can be avoided.

“We wouldn’t be entering into these rounds of talks or negotiations unless that was our objective,” she said.

“I don’t think there is an appetite out there for a general election.”

Any deal between the traditional main parties would likely also require the support of the Green Party.

The Greens are also due to open “detailed” talks with Sinn Féin on proposals for a programme for government.