Senior figures in Fine Gael and Fianna Fail have both ruled out the parties going into power together despite a former government minister claiming it is inevitable.
Fianna Fail leader Micheal Martin reiterated his vow to work in the national interest whatever the outcome of the election but dismissed any possibility of a pact with their old rivals.
He also insisted his party would not share power with Sinn Fein as part of any post-election deal.
"No deal with Fine Gael, no deal with Sinn Fein," he said.
But Mr Martin said Fianna Fail would work with the next government "in whatever capacity the electorate give us".
"We will behave responsibly in the interest of the country," he added.
"We are going to win as many votes and seats as we can. It is important we debate the kind of society we want, the issues, rather than the horse trading."
Separately on day 16 of the election campaign, Fine Gael Finance Minister Michael Noonan was categorical in his ruling out a coalition with Fianna Fail.
"Never. Never is the word," he said.
Despite the no love lost routine between the old adversaries, former Fianna Fail minister and founding Progressive Democrat leader Des O'Malley said the claims should be taken with "two or three pinches of salt".
Mr O'Malley said he could see Fine Gael and Fianna Fail, whose enmity stretches back to the civil war, hammering out a deal with each other if each are unable to form a strong government with other parties.
"I could see it happening, yes," he told RTE's Campaign Today.
"It may well happen and it will give, I suppose, a certain stability to the country."
He added: "It is going to be inevitable if we are going to have a government, I think there'll have to be a coalition."
The three-times government minister said parties can not "throw back in the face of the electorate" the outcome of the general election.
Under Mr O'Malley, the Progressive Democrats formed a coalition with Fianna Fail leader Charlie Haughey in 1989.
He said the parties had a duty to respond to the mathematics of the election at the time as that was what the people had decided.