Sinn Féin leader Mary Lou McDonald has described comments by the Fine Gael leader about her party's public meeting in Cork as "a hysterical overreaction".
The party said it plans to have a series of public meetings over the next two weeks to update supporters about their efforts to form a government.
Taoiseach Leo Varadkar said the rallies are "designed to be the next phase in Sinn Féin's campaign of intimidation and bullying".
Speaking before the meeting tonight, which was attended by close to 1,000 people, Ms McDonald said: "Mr Varadkar's comments were over the top and were a demonstration by him and by a political establishment who are desperately reaching for something to stop an unstoppable change in Irish politics."
Ms McDonald rejected suggestions that the meeting was about whipping up support for Sinn Féin.
She said it was about continuing a conversation, which she began with the electorate during the election.
Ms McDonald said she saw no reason why the conversation with the electorate could not continue after the election and she said the attitude displayed by Mr Varadkar was the very thing which built cynicism in politics.
People continuing to arrive half an hour after the Sinn Féin meeting in #Cork kicked off. Not far off a thousand people here now. Extra chairs were wheeled in, adding to the 372 originally put out and many people are standing at the sides and at the back of the hall. @rtenews pic.twitter.com/kQbwKTcd4y— Paschal Sheehy (@PaschalSheehy) February 24, 2020
Earlier, Mr Varadkar said plans by Sinn Féin to hold rallies across the country are "an unwelcome development".
Mr Varadkar said the rallies are "designed to be the next phase in Sinn Féin's campaign of intimidation and bullying".
He added: "I wouldn't be surprised if their next step is to take to the streets."
Speaking at an event in Dublin, Mr Varadkar said: "It shows once again this is not a normal party."
Sinn Féin is planning five rallies, with the first in Cork tonight and the others in Dublin, Galway, Cavan and Newry.
Sinn Féin's finance spokesperson Pearse Doherty described Mr Varadkar's comments as "hysterics".
Mr Doherty said they were just public meetings and involved elected representatives going out to meet people who voted for them.
Sinn Féin's Pearse Doherty describes Leo Varadkar's comments as "hysterics". Says their rallies are just public meetings and involve them going out and taking to voters. @rtenews pic.twitter.com/yimsbRjiVt— Sandra Hurley (@sandra_hurley) February 24, 2020
He said the difference between them and other political parties was that when the election was over, they did not close the doors of Government Buildings.
He said he very much welcomed that Mr Varadkar and Fianna Fáil leader Micheál Martin had given "huge publicity" to their meetings.
"The hysterics from Leo and Micheál are just that, nothing but hysterics", he said, adding that they feared change.
Mr Doherty said they were not aware of any orchestrated Sinn Féin-member bullying of people online and if there was, they would deal with it.
Mr Doherty also said they were intensifying detailed discussions with other parties and independents this week and they had engaged this morning with the Green Party on detailed policy issues.
Asked about the difference between Sinn Féin and the Green Party on carbon tax, he said they were opposed to the tax because the alternatives were not there. But he said they both were taking the climate agenda very seriously.
Yesterday, Sinn Féin's deputy leader Michelle O'Neill said the party will set out its stall at the rallies and "people will have an opportunity to come along, those who support us and those who don't".
Mr Varadkar also said talks between Fine Gael and Fianna Fáil this week are "just exploratory discussions" and do not signal a change in approach by his party to government formation.
He said Fine Gael was preparing for opposition, but added that "the party is willing to engage in exploratory talks with any party that wants to talk" to it.
Mr Varadkar said "the onus still falls with Sinn Féin to form a government".
He said: "Sinn Féin and the left believe that they won the election, they have an opportunity to prove that now by forming a government."
He said if they cannot do that, they should "fess up and say they didn't actually win the election".
On Brexit, Mr Varadkar insisted "there can be no backsliding" on the Northern Ireland protocol in the Withdrawal Agreement.
Mr Varadkar's comments come following reports in the British media that Prime Minister Boris Johnson's Brexit team has been ordered to come up with plans to "get around" the protocol.
He said the Withdrawal Agreement is an international treaty and he said "we expect the British government to honour that in full".
The Taoiseach said "lets focus instead on the next phase, which is negotiating a free-trade agreement" between the EU and the UK.
Additional reporting: Sandra Hurley and Fergal O'Brien