Fianna Fáil Director of Elections Jack Chambers said there is growing confidence that the party will remain the largest in local government when all the votes are counted, and the full democratic process has concluded.
"We are in a really strong position as the final seats are declared," he said, as as the counting of votes approaches the finish line.
Just after 9pm, Fianna Fáil and Fine Gael had 234 seats each with just 40 seats left to fill.
With almost 95% of local election seats filled around the country, Fine Gael are leading the way with 23% of first preference votes while Fianna Fáil have 22.9%.
Sinn Féin had 99 councillors returned just after 9pm as they pulled well clear of Labour, at 55, to be the third largest party in local government.
Tánaiste Micheál Martin said the Government is focused on the budget and not a general election despite Fianna Fáil and Fine Gael performing strongly in the local and Europeans.
Mr Martin also said he looks forward to the prospect of contesting any by-elections that may arise from the European contest, but suggested the Government may wait some time before they run these contests.
"I think we are going to stay focused. Local elections are different to general elections. Our focus will be on the budget, preparing a financial framework for that. That's going to be very challenging with lots of pressure on expenditure particularly in health and housing."
Mr Martin said that while May and June are the optimal time for an election, they have passed and he appeared to suggest the Government would wait a number of months before running any by-elections
"Actually I like by-elections. Anyone who studies political science knows that by-elections can be significant platforms for new candidates. I think we'll settle down now for a while and get back to governing. We need to govern. The budget is key."
The Tánaiste also said that he believes Sinn Féin's lack of policies contributed to its performance and he said the results show that opinion polls should not be relied upon
"I think Sinn Féin haven't really produced solutions. If you look at their policy positions they're very threadbare, there's no substance. I don't see substantive policies coming from Sinn Féin on a whole range of issues."
The Tánaiste also would not be drawn on who he would select for the EU Commissioner position, but said he would consult with his party on the issue.
Sinn Féin is likely to finish with more councillors than in 2019 - but with fewer than the party envisioned at the start of campaigning this time around.
Meanwhile, the Social Democrats has seen more than 30 of their candidates elected, the bulk of which have won seats in the east of the country.
Twenty-four members of Independent Ireland have been elected so far.
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For the other government party, the Green Party, it appears likely to hold relatively steady with 21 candidates elected.
Fifteen local authorities have completed counting, including the largest one - Dublin City Council.
Cork City Council along with the City and County Councils of Waterford and Limerick have finished their counts.
Clare, Cavan, Galway, Kilkenny, Leitrim, Louth, Monaghan, Sligo, South Dublin, Tipperary and Wicklow County Councils are all also finished.
Fine Gael Minister of State and Government chief whip Hildegarde Naughton said the public was craving "stability" as she insisted an early general election as not on her party's mind.
"That's the strong message that we're getting. So we really do have a lot of work to do in relation to this and elections are not on our mind," she said.
The TD for Galway West added: "We have a programme for government that we need to deliver, a huge amount has been delivered to date.
"But a lot of this legislation does take time to get over the line and we have such an amount of bills to get through right up to mid-July and also when we are back in the Dáil in September. So we really need to finish off that work."
Date for general election should be agreed between coalition leaders - McGrath
Minister for Finance Michael McGrath said a decision on the date of the general election should be decided by agreement between the coalition leaders Simon Harris, Micheál Martin and Eamon Ryan.
Mr McGrath said it was important that the Government's term ends well and that relationships remain strong.
Speaking to RTÉ News at the Ireland South count centre in Cork, Mr McGrath said he recognised that the date of the general election was a matter for the Taoiseach, but he added: "I do think the decision in the end should be by agreement.
"While it is the constitutional prerogative of the Taoiseach, he has made it very clear he will consult and engage with the Tánaiste and with Minister Ryan.
"I think it's important that the term of the Government ends well, and that relationships are strong at the end, as they have been right the way through."
Local election results did not match party's ambition - McDonald
Sinn Féin leader Mary Lou McDonald said the results of the local elections did not match the ambition the party went into the election with.
Ms McDonald admitted it was a bruising weekend for the party, however, the party was winning council seats in areas where they previously had none.
"I'm disappointed that we didn't get more of our wonderful slate of candidates elected... It's important now that we reflect on what we have been told on the doorsteps, our own performances and we efficiently regroup and go back at it again," she said.
While acknowledging that Sinn Féin may have ran too many candidates, Ms McDonald praised them for putting in a "hard shift", describing their efforts as "very energetic".
In the European elections, Ms McDonald said she believed Lynn Boylan would win back the European Parliament she lost in 2019 in Dublin. She added that the party was also in the mix in Ireland South.
