First Minister Arlene Foster believes Sinn Féin’s proposals for an investigation into NI’s controversial heating scheme could work.
But she has rejected calls to step aside while it is investigated.
The flawed Renewable Heating Incentive (RHI) scheme could cost taxpayers £490m.
Sinn Féin has published its proposed terms of reference for an independent investigation into the scheme.
Mrs Foster set up the scheme in 2012 when she was enterprise minister.
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It was an attempt by the NI Executive to increase consumption of heat from renewable sources.
But businesses received more in subsidies than they paid for fuel, and the scheme became heavily oversubscribed.
Justice Minister Claire Sugden said on Friday she did “not have the power” to initiate a public inquiry into the scheme.
Finance Minister Máirtín Ó Muilleoir warned earlier that if Mrs Foster does not step aside temporarily, an election would be inevitable.
When asked on Friday if she would accept the proposals, Arlene Foster replied firmly: “No.”
Later, she released a statement saying: “With the exception of the issue of stepping aside, we believe that the proposals provided to us by Sinn Féin provide a basis for taking an investigation forward.
“Officials have raised a number of technical issues in relation to the proposals, however there do not appear to us to be any insuperable obstacles to agreement being reached.
“Other parties have suggested that, rather than the Attorney General appointing a judicial figure, this appointment function be undertaken by the Lord Chief Justice.
“We would be equally comfortable with this proposal.”
On Friday evening, Sinn Féin MLA Carál Ní Chuilín said there could not be any agreement unless Mrs Foster stepped aside.
However, the DUP has consistently rejected calls for Mrs Foster to step aside.
“We have yet to be notified that our full terms of reference are agreed,” Ms Ní Chuilín said.
“Sinn Féin has also made it clear that Arlene Foster needs to stand aside pending a preliminary report from the independent investigation which must have the powers to compel witnesses and evidence.”
On Friday, a defiant Mrs Foster posted a picture on Facebook of a guinea pig wearing a pair of pink love-heart shaped glasses below the phrase: “Can’t see all the haters when I’ve got my love glasses on.”
Alliance leader Naomi Long responded to the post, saying: “They’re not haters, they’re taxpayers. And angry ones at that.
“We’re in the teeth of a financial crisis, much of it of her making, and the first minister opts for this by way of a response to her critics?”
On Wednesday, Economy Minister Simon Hamilton said he and Mrs Foster had come up with a plan to limit public losses to “effectively zero”.
Under the terms of power sharing outlined in the Good Friday Agreement, Sinn Féin and the DUP hold joint office at the head of the Northern Ireland Executive and must both agree on how to investigate the RHI crisis.
Sinn Féin has previously rejected the terms of reference drawn up by the head of the Northern Ireland civil service to investigate the issue.
The party wants the attorney general to appoint a judge to head up the panel.
Emergency legislation would be required to give the investigation the powers to compel witnesses and documentation.
The party said this could be done under accelerated passage; it wants the panel to produce a preliminary report within four weeks and a final report within three months.
“If Arlene Foster wants to do the right thing, then the right thing to do would be to step aside,” said Sinn Féin’s Michelle O’Neill.
When asked if any investigation could go ahead without Mrs Foster standing side, she replied: “No”.
“The public needs to have confidence and faith that any investigation that takes place is full transparent,” she said.
“Our terms of reference clearly sets out a judicial figure, independent of any minister or any of the executive, will take forward an investigation.
“But at the heart of that has to be the issue of compellability, because if they can’t compel people and papers, then the investigation’s not going to be worth the paper it’s written on.”
Some hearings could be held in public but that would be up to the panel to decide, added Mrs O’Neill.
The proposal to resolve the controversial renewable heating scheme was denounced by Mr Ó Muilleoir as a “sticking plaster” after “clear the air” talks with Mr Hamilton on Thursday.