FORMER First Minister Arlene Foster has sought to save the Stormont institutions by saying she is open to make-or-break talks with Sinn Féin.
The DUP leader also signalled her support for a public inquiry into the Renewable Heat Incentive (RHI), in a shift in her stance on how the botched scheme should be investigated.
But Gerry Adams said on Tuesday that he believes an election is necessary and there is no prospect of Sinn Féin helping avert a snap poll by nominating a deputy first minister ahead of Monday's deadline.
Secretary of State James Brokenshire will try over the coming days to bring together Stormont's two big parties in an effort to rescue the government but the Sinn Féin leader said there was little point.
Mr Adams told The Irish News that Mrs Foster needed to be held accountable for the RHI's failings and ways found of stemming the hundreds of millions of pounds committed to the scheme.
He said the DUP leader's call for a public inquiry was overdue and Sinn Féin had set out its proposals for a robust investigation, modelled on a commission of inquiry carried out in the Republic.
The Louth TD blamed Mrs Foster's refusal to step aside for the latest Stormont crisis.
"When you get a scandal to the tune of half a billion pounds sterling it has to be dealt with, there has to be transparency, that has to be protected."
Asked about the prospect of an eleventh hour nomination for the deputy first minister's role, he replied: "I can't see that happening".
He said Sinn Féin would join Mrs Foster in a future executive if an inquiry into the RHI cleared her, but there could be "no return to the status quo".
As Mr Adams was speaking to the media on Belfast's Falls Road, across the city at DUP headquarters the former first minister was holding a press conference to which The Irish News did not get an invite.
Mrs Foster said she supported the establishment of a public inquiry under the 2005 Inquiries Act and said it could take place without the approval of Sinn Féin.
It was reported that she said an unnamed minister would announce an investigation within 24 hours.
"We are willing to take part with any discussion to see if a way forward can be found," she said.
"I remain open to further discussions with Sinn Féin or any of the other parties in the assembly over the next few days."
The DUP leader said confidence in the institutions needed to be restored and that her personal personal integrity retained.
Predicting that an election would be "brutal" and there would "undoubtedly" be a period of direct rule, she said she been "completely maligned over this past number of weeks and months".
However, Sinn Féin health minister Michelle O’Neill described Mrs Foster's intervention as "an act of desperation".
"If the DUP were serious about addressing the political crisis then Arlene Foster would have stepped aside a month ago as Martin McGuinness suggested privately to her," she said.
"They refused to do so and arrogantly attempted to brazen out the public anger."
TUV leader Jim Allister also described the DUP's support for a public inquiry was "electioneering pure and simple", contrasting it to Edwin Poots's assertion in the assembly on December 19 that "there will not be a public inquiry".
Ulster Unionist leader Mike Nesbitt said he could see no prospect of the DUP and Sinn Fein working together and the next executive should be formed by "two parties representing our two traditional communities who want to work together for the common good".
Alliance leader Naomi Long claimed Mrs Foster's inquiry call was “too little, too late” ahead of a potential election and it was "questionable whether Arlene Foster even has the power to initiate such an inquiry now".
Meanwhile, finance minister Mairtin O Muilleoir said a paper from the Department for the Economy on solutions to the RHI overspend was "submitted to my department at 5:55pm on Monday but withdrawn 10 minutes later".
He also said poultry firm Moy Park had "briefed my officials in relation to new concerns over the RHI scheme".
Moy Park said in a statement that many of its contracted farms are RHI claimants and "as advocates of the responsible use of heat, we felt our experience could be relevant and useful in the development of a solution".
