Sinn Fein leader Gerry Adams has said the "perpetual unionist majority" at Stormont has been "demolished" following the result of the Northern Ireland Assembly election.
A jubilant Mr Adams said it was a "watershed" moment after his party closed to within a solitary seat of the Democratic Unionist Party.
He also said Sinn Fein's new leader in the north, Michelle O'Neill, will be holding talks with Prime Minister Theresa May and Irish Taoiseach Enda Kenny about the impact of Brexit on Ireland north and south over the next few weeks.
Speaking outside the party's West Belfast office, Mr Adams said Sinn Fein wants to quickly engage in a process with other party leaders to ensure powersharing in the region is restored.
But he again insisted that the party will not support DUP leader Arlene Foster as Northern Ireland's first minister until she has been cleared of any wrongdoing related to the Renewable Heat Incentive (RHI) scandal.
However, it could leave the executive in limbo for up to a year, as it emerges that the inquiry into RHI will not supply any preliminary findings to speed the process along.
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"There is a need for this inquiry to come to conclusions before we can nominate (Arlene Foster) for a position of first minister," said Mr Adams.
He added: "The first position we put was that Arlene Foster stand aside until a preliminary report. Now we are being told there will be no preliminary report.
"Our position is very straightforward. We will not be consenting to Arlene Foster being first minister until this issue is cleared up."
He added that "what was good enough for Peter Robinson (who twice stood aside as first minister amid controversy) is good enough for Arlene Foster".
Ms O'Neill, who replaced Martin McGuinness in January, said she is to hold talks with both the British and Irish governments to discuss the way forward for the region's political institutions.
"I also made contact with the leaders of all the political parties to talk about next week and how we are going to conduct ourselves in the time ahead.
"We obviously have a period of three weeks in front of us and whilst the task isn't going to be easy it is achievable if people come at it with the right attitude.
"On Monday morning I will lead our team into the assembly where we are ready to deal with all the issues," she added.
The pro-Brexit DUP narrowly remained the region's largest party by just one seat as a Sinn Fein surge saw the republican party make major gains over the DUP.
Having entered the election 10 seats ahead of Sinn Fein, the DUP's advantage was slashed to a solitary seat.
DUP MP Sir Jeffrey Donaldson has insisted there is no question over Ms Foster's future as party leader despite the party's disappointing performance.
Mr Donaldson said that despite the bruising election the DUP is still the largest party and their focus now "is on Arlene and the party getting a government up and running again at Stormont".
"I must say, I am not aware of any election in the past where the leader of the largest party resigns because they have won the election.
"We need to learn the lesson and understand what people were saying in this election and what the key messages are.
"We have been given the responsibility as the main party to take the lead at Stormont and that is what we intend to do so we are not going to get bogged down on what some people want to focus on, which is personalities.
"Arlene is leading the largest party and we need to get on with the job of forming a government that works for us all," said Mr Donaldson.
Sinn Fein and the DUP now have three weeks to establish a government.
If a government cannot be formed between the two main parties within that time then, under law, another election will be called.
However, Mr Donaldson said he does not believe Westminster will want another election.
"If we can't get a government formed within three weeks I don't think the Westminster government will allow another election. I think they will introduce direct rule.
"We are determined to work to achieve (a powersharing government) but if it doesn't happen I fear we could be looking at a lengthy period of direct rule."
Only 1,168 first preference votes separated the DUP and Sinn Fein and, for the first time, Unionists will not have an overall majority at Stormont.
Amid the fallout, Mike Nesbitt said he would resign as Ulster Unionist leader.
It was a positive campaign for both the SDLP and Alliance who both maintained their seats.
The election was called after the collapse of a coalition led by Arlene Foster's DUP and Sinn Fein's Martin McGuinness.
Mr McGuinness resigned over Ms Foster's refusal to step aside as first minister pending an inquiry into the Renewable Heat Incentive (RHI) scheme, which could cost the Northern Ireland taxpayers £490m.