Fianna Fail leader Micheal Martin has yet to respond to the Sinn Fein leader’s invitation to discuss the possibility of forming a coalition.
Sinn Fein’s Mary Lou McDonald said the time for other parties to say they will not speak to them about forming a government is over, following the party’s election success.
Fine Gael and Fianna Fail have repeatedly ruled out going into government with Sinn Fein as talks begin this week to try to form a coalition government.
Fianna Fail won the most seats with 38, but Sinn Fein won 37 seats and the highest proportion of first preference votes following Saturday’s general election.
Speaking in Dublin following a meeting of the new Sinn Fein parliamentary party, Ms McDonald said: “We are stepping our way through a process where we work out what this government for change might look like.
“My first preference is for a government without Fianna Fail or Fine Gael. The seats are now filled and it looks like it would be tricky to form such a government.
“I have written to Micheal Martin and have not had any response to that correspondence, but I hope to meet with him.
“There are huge differences between ourselves and Fianna Fail.
“The question that arises in the midst of all of this is whether or not Fianna Fail can actually be a part of and commit to that appetite for change and good delivery for citizens on the ground.
“Micheal Martin has adopted a position that I believe is so far untenable to say that he would not speak to us.
“We represent such a significant section of Irish opinion and I think anybody who followed and participated in the election cannot have missed the appetite for change, it was writ large – everybody agreed that that was fundamentally the theme of the election.”
Speaking on Thursday morning, Ms McDonald said: “We are not like those in politics for power or status. We’re not like those that have spent decades in government serving their own interests.
“That is old politics, that is politics of the past – where government came and went but the age-old problems remain.
“That is why Fianna Fail and Fine Gael were so determined to keep us out of government. They said they wouldn’t talk to us. Some of them still say it.
“That they will ignore the democratic mandate, but that stance has run out of road. Those days are over, now is the moment for change, now is our time.”
She said a referendum on Irish unity is a key part of the Good Friday Agreement and preparations must begin.
“It is a duty of the Irish government to commence this process. Unionists should not fear a debate and discussions about the future.”
Ms McDonald has written to Mr Martin as party talks continue on Thursday to form a government.
The Fianna Fail parliamentary party will meet later on Thursday but Mr Martin has repeatedly ruled out going into coalition with Sinn Fein.
Taoiseach Leo Varadkar said on Wednesday he expects to be the leader of the opposition in the next Irish parliament – which would mean Fianna Fail and Sinn Fein are the most likely coalition partners.
Mr Varadkar said “anything is possible” in the coming weeks, including a second election, but added it would “not be good for the country”.
Sinn Fein TD Pearse Doherty said on Thursday that Ms McDonald had contacted Mr Martin.
He said in a statement: “Sinn Fein is looking to establish a government for change. Now we wish to meet with Fianna Fail, and later on with Fine Gael. The first step of that process is for our leader Mary Lou McDonald to meet with the leader of Fianna Fail, Micheal Martin.”