Taoiseach Leo Varadkar has hit out at Sinn Féin's plans to hold rallies, describing them as a campaign of "intimation and bullying".
The party has organised a number of public meetings on both sides of the Irish border to drum up support in its bid to be part of the next government.
The first public rally will be held in Cork later on Monday.
Mr Varadkar said the plans are an "unwelcome development".
"Generally what happens in a democracy is people vote, the votes are counted and then parties try to form a government," he said.
"What's happening here ... it seems that Sinn Féin, having won less than a quarter of the vote, are behaving as if they have won a majority.
"My party regularly won more than a quarter of the vote and didn't get into government.
"I think these rallies are designed to be the next phase in Sinn Féin's campaign of intimation and bullying.
"We saw that online and now we are seeing it in their rallies, and I wouldn't be surprised if the next step is that they take it to the streets.
"It just shows you, again, that they are not a normal party; this is a party that has a casual relationship with democracy."
Mr Varadkar is meeting Fianna Fáil leader Micheál Martin on Tuesday.
The Fine Gael leader previously said his party was preparing to go into opposition.
Mr Varadkar denied that the meeting between the two leaders was a change in Fine Gael's approach to government.
"As I said last week, we would be willing to engage in exploratory talks with any party that wants to speak to us," he said.
"That's happening with Fianna Fáil and the Greens this week. Labour have their own issues and don't want to talk, and Social Democrats cancelled their meeting we offered them, so really it's just exploratory discussions at this point with Fianna Fáil and the Greens this week.
"What I would say is that the onus really still falls with Sinn Féin to form a government.
"They on the left believe they won the election, they have an opportunity now to prove that now by forming a government, and if they can't form a government they should fess up and say they didn't actually win the election, and even if they had they disagree with each other so much that they wouldn't have been able to form a government anyway."
Mr Varadkar was speaking at event where Mastercard confirmed it is creating 1,500 jobs in Ireland over the coming years.
Asked where all the newly recruited staff would live in Dublin, Mr Varadkar said that one of the "features" of a strong economy was the pressure on housing.
He also hit out at other political parties' housing pledges made during the general election.
"We have heard a lot of people in the last couple of months making out that they can magic up houses overnight or even within a few weeks; that isn't true. We are going to stick to what is true, and that is continuing to scale up an increase of number of new homes," he added.
Meanwhile, Northern Ireland Secretary Brandon Lewis refused to be drawn on whether he agrees with the PSNI's report that the IRA Provisional Army Council still oversees Sinn Fein.
It comes after Garda Commissioner Drew Harris said his force's assessment of the report "does not differ" from the PSNI's.
Mr Lewis was asked about his view of the report during a visit to Derry on Monday.
"We got the assessment from 2015, I've got nothing to add from that," Mr Lewis said.
"I think there has been a lot of coverage of that over the last period. My focus is about looking forward."