LEO Varadkar and Micheál Martin clashed with Mary Lou McDonald during a pre-election leaders' debate.
The live RTÉ debate involving seven party leaders saw Fine Gael and Fianna Fáil challenged over why both say they are not considering a potential coalition government with Sinn Féin following the Irish General Election.
Mrs McDonald accused Fine Gael and Fianna Fáil of "arrogance" and "hypocrisy" by ruling out her party as coalition partners.
"There is something incredibly arrogant, obvious even, when leaders of other parties believe that we can be disregarded," she said.
"It is also deeply hypocritical, of course, because those same party leaders go up and warmly shake the hand of Sinn Féin ministers in government in the north.
"At the end of the election I will speak to everybody, I will listen to everybody and my objective will be to deliver a republican programme for government."
Mr Varadkar responded by telling Ms McDonald: "It isn't anything personal.
"It is entirely based on policy and principles and the reason why my party wouldn't be in a position to form a coalition with Sinn Féin is that, in our view, Sinn Féin is soft on crime and high on taxes, for example, doesn't support the Special Criminal Court, the court that we are going to use to lock up some of the drug lords that are causing some of the violent crime that we are seeing around the country at the moment, and they are also a party that consistently looks for higher taxes on business and on incomes, and we don't think that is the right way to go."
Mr Martin said: "I would say [is] SF extremely arrogant to say we or Fine Gael owe them a place in power. We don't.
"The reason why Sinn Féin have opposed the Offences Against the State Act and the Special Criminal Court year after year since they came into the Dáil is because the Provisionals within their movement wouldn't allow them to vote for it.
"That's it, the old provos hate the Special Criminal Court. Why? Because the Special Criminal Court defeated the Provisional IRA in the Republic. Let's call a spade a spade."
Labour Party leader Brendan Howlin said he would not rule any party out of coalition, describing that as "arrogant".
"After this election, we could have a block of 25 TDs that would include the Social Democrats and People Before Profit," he said.
"There is very little we disagree on, if we had critical mass we could form a progressive government."
People Before Profit candidate Richard Boyd-Barrett hit out at the Labour Party for "imposing crippling austerity" on the Irish people the last time it was in a coalition government with Fine Gael.
Green Party leader Eamon Ryan said the future of politics and society will be different but it will require "radical change".
He said he would not rule out working with any particular party as every group has a duty to deal with the climate crisis.
Social Democrats leader Roisin Shortall said no-one has the right to veto who they will or will not go into government with.
She said: "There is a responsibility on all government parties to work together to address the huge societal issues we face and reach solutions to the health service, the housing crisis and climate change.
"It is wrong to say we will not work with this person or that person."
The two-hour live debate also saw leaders clash on housing, the Garda, taxation policies, health and the pension age.
Earlier during a visit to Dublin, EU chief Brexit negotiator Michel Barnier rejected claims that a change in government in Ireland would be a concern for the Brexit process.
"Frankly speaking, as an EU negotiator I always worked with each and every other EU27 member state with elected governments," he said.
"I will continue to work with the government chosen by the citizens."