Mary Lou McDonald has said it is still possible to have a Sinn Fein-led government despite the numbers making such an administration difficult.
The Sinn Fein leader said talks will intensify with smaller parties this week in a bid to form a left-leaning government.
Speaking in Dublin on Monday morning, she said: "There is undoubtedly a solid block of TDs for change for a new government.
"I remain very determined that we deliver that government. And I think that we need to knuckle down on the policy issues - on housing, on the need to cut rents and freeze them, on the need to deliver a huge public housing programme and on the need to resolve the issue around pensions and get it back to the age of 65.
"We are still very determined that an alternative and a new government of change can be created. And we will intensify our efforts this week when we have conversations with other parties.
"I am very clear that we have been elected in very large numbers to be in government, even to lead the next government.
"I've also said that the idea of seeing Fine Gael or Fianna Fail returned again for five years is unthinkable.
"We can speculate on many, many things but but I think we can be clear that the outgoing government was deeply unpopular and failed people in many and profound ways, and that people voted for change."
Ms McDonald said there is little public appetite for an election but that Sinn Fein will fight one if required.
"I want to see a good, stable strong government that can deliver on housing, on health, can deliver on the issues that matter to people. But if there is an election, I mean we'll go and we'll fight the election."
