All 160 seats have been filled, with FF (38) ahead of SF (37) by a single seat, while FG has 35
The UK needs to start preparing for a united Ireland in the aftermath of Sinn Fein's success in the Irish election, Mary Lou McDonald warned on Monday night.
The Sinn Fein leader, fresh from her triumphant general election in the Republic, also took aim at whoever ends up as the next Taoiseach, telling them that they must push for a united Ireland.
In an interview with BBC Newsnight, Ms McDonald said: "Those on the island of Britain, and in London in particular, need to start preparing, because constitutional change is coming.
"The point has been conceded in the Good Friday Agreement by the British state - the presence here is solely on the basis of consent.
"That consent can only be tested in a unity referendum and we are going to have a unity referendum, and I want us to do it in an orderly, thoughtful, democratic and absolutely peaceful manner.
"Whoever is Taoiseach when all of this plays out needs to make that case very plainly and very clearly to Boris Johnson."
Ms McDonald called Brexit "a mess" and said the EU "needs to take a stand in respect of Ireland in the same way that it supported the reunification of Germany".
She added: "This is live, this is happening and if anybody imagines that this issue can be wished away or that we can simply carry on regardless, they are very, very foolish.
"In fact, I would go so far to say that it's irresponsible now at this stage not to plan for constitutional transition."
Earlier Ms McDonald predicted she herself could be poised to become Taoiseach. The Sinn Fein president insisted she may lead a new government as her party continued to bask in a remarkable general election result that saw it top the popular vote, shattering Fianna Fail and Fine Gael's long-time grip on power.
On an impromptu walkabout in Dublin city centre, Ms McDonald said: "I may well be the next Taoiseach, yes."
She later told the media: "I think it would be a mighty thing to have a Sinn Fein Taoiseach and also a woman perhaps in the job, but you might say she would say that wouldn't she?"
Asked whether she believes she can lead a government, Ms McDonald responded: "The numbers will tell me that when the numbers are finally tallied."
Counting continued on Monday and by 8.40pm 146 of the Dail's 160 seats were filled.
Despite receiving the most first preference votes, Sinn Fein's place in the next government is not guaranteed.
The party failed to run enough candidates to capitalise on its surging popularity in Ireland, so it will not finish up with the most seats.
Fianna Fail is on course to be the largest party, though Sinn Fein could finish in second place behind outgoing Taoiseach Leo Varadkar's Fine Gael, the big loser of the poll.
All three parties will fall well short of reaching the 80 seats required for a Dail majority so, barring another election, some form of coalition is inevitable.
The task of forming a government could be a long and tortuous one and may force either Fianna Fail or Fine Gael to back-track on long-standing pledges never to do business with Sinn Fein.
On Monday, a senior Fianna Fail politician described a coalition with Sinn Fein as "untenable".
Jim O'Callaghan also insisted party leader Micheal Martin had not softened his stance on ruling out the party as government partners.
"We need to recognise we gave a commitment and when you look at the policy differences between Sinn Fein and Fianna Fail, I don't think it's tenable to suggest that we should be in coalition with them," he said.
Mr O'Callaghan's views are not echoed by all his colleagues, with some Fianna Fail members having indicated a willingness to do business with the party.
Mr Martin later cautioned observers not to "jump the gun" in interpreting his remarks as a signal an alliance with the party was in the offing.
Meanwhile, Garda Commissioner Drew Harris has said he would work with a Sinn Féin Justice Minister "to provide for the security of the country".
The former PSNI Deputy Chief Constable was speaking after Sinn Féin recorded the highest number of first preference votes in the general election, making it a likely coalition partner in the next government.
Mr Harris's father Alwyn Harris was murdered by an IRA car bomb in 1989 while on sick leave as an RUC superintendent.
The bomb exploded under the family car as Alwyn Harris and his wife drove to a Sunday church service. Mr Harris died while his wife survived the blast.
Speaking in Dublin, Commissioner Harris said: "I'm here to protect democracy and to keep people safe. So whatever minister we have I'm sure we'll have a positive working relationship."
Elsewhere, a Sinn Fein TD who was filmed shouting "Up the Ra" during a victory speech has defended the comment, saying it happened during "the excitement of the night".
Waterford TD David Cullinane was recorded making the comment as he spoke to supporters hours after he was elected.
He said Sunday was a "very emotional day" for him but that the comments were not about the future. The short clip was posted on social media on Monday.
"Obviously we were very excited and very proud of the vote we got in Waterford," Mr Cullinane said. The party's Brexit spokesman refused to apologise, saying he was "reflecting" on that time period.
Ms McDonald denied suggestions that the controversial video will hinder the talks process ahead.
Only the bitter and shortsighted would try to take away from what was a stunning performance by Sinn Fein in the Irish general election. Their victory doesn't threaten Irish democracy. It certainly bears no resemblance to the rise of fascism, or National Socialism, in the 1930s.
Sinn Fein supporters are in cheery form this week because of their astonishing performance in the southern election. And some of them are in smug form, too, delighted by the failure of what they saw as a strategy to damage the party.