Arlene Foster's position as First Minister in the next Assembly will only be discussed once overall agreement has been reached, Sinn Fein president Gerry Adams has said.
His party collapsed the power-sharing institutions after Martin McGuinness's request for the DUP leader to step aside while a botched green energy scheme was investigated was denied.
Stormont's politicians are considering how to implement measures dealing with past killings and a range of other issues as the deadline looms for a deal to rescue the devolved administration before fresh elections are called.
Mrs Foster said earlier this week the post in the next Assembly had not been raised by republicans with her.
Mr Adams said: "In terms of the sequence here it only comes into the radar if there is an agreement.
"We don't have an agreement yet. Let's get the agreement."
DUP leader Arlene Foster said she was in solution-finding mode.
She said: "If we are telling each other who we can and cannot nominate, then we will have something to say about the Sinn Fein nominees as well.
"We are focused on devolution, we are focused on finding solutions.
"We are in solution-finding mode, that is where we are and we hope that everybody else is as well."
Deputy DUP leader Nigel Dodds said the atmosphere between the parties was businesslike and constructive.
Almost half a billion pounds worth of taxpayers' money could be overspent on the failed Renewable Heat Incentive (RHI) scheme, which is expected to pay out more in subsidies than the green fuel costs.
A public inquiry into the matter has begun work and the judge chairing it has said it will take more than six months to report.
Mr Adams added: "Clearly, the inquiry is under way or at least it will be ongoing in the course of all of this and the issue of putting together an Executive does not arise until we have an agreement."
Mrs Foster was the minister responsible when the scheme designed to promote the use of green energy was drawn up. No wrongdoing is suggested.
Sinn Fein has vowed not to enter power-sharing with the DUP leader as First Minister until the scheme which left some businesses in line for a windfall is investigated.
Mr Adams added: "That only becomes an issue if we have an agreement.
"As Michelle O'Neill has said, our endeavour here as part of these implementation talks is to get an agreement. Let that be the focus.
"The focus is to get the terms where we can go back, not to the status quo but to the way the institutions should have been run.
"That is our focus, we have not gotten there yet, that is where we want to be."
The parties have three weeks to form another ministerial Executive or Secretary of State James Brokenshire may call another election.
Sinn Féin said this week it would "unacceptable" for Mrs Foster to be part of an executive while the public inquiry into the botched Renewable Heat Incentive scheme continues.
The Irish News asked all the other parties represented at Stormont, as well as the sole independent MLA, if they would support the DUP leader as first minister.
Independent unionist Claire Sugden, who agreed to serve as justice minister with the DUP and Sinn Féin in the last executive, said it was matter for Mrs Foster.
However, the East Derry MLA added that she is "now becoming the story".
"It should not be about that, it should be the people of Northern Ireland and how we can move forward and if she is providing a distraction to that then I think there is a leadership decision she has to take," she said
Last month SDLP leader Colum Eastwood said Mrs Foster cannot return to the role of first minister while an RHI inquiry is ongoing.
"Arlene Foster can't just expect to step back into government. She needs to step aside until that public inquiry reports," he said.
Green Party leader Steven Agnew also said yesterday that Arlene Foster should wait until the inquiry ends.
“Arlene Foster should create breathing space for everyone by holding off any return as first minister until after the RHI inquiry has concluded – this was the verdict of the bulk of the people during the election and something that the DUP leader should not ignore."
People for Profit's sole MLA Gerry Carroll said "under no circumstances" should Arlene Foster be re-instated as first minister, even temporarily.
The Alliance Party said it has not asked Mrs Foster to step aside but "suggested that she should in order to allow a clear investigation to take place".
"For Alliance this is not about personalities and preconditions, but policies and practice."
The Ulster Unionist Party said it was "entirely a matter for the DUP as to who it nominates as its choice for first minister", although before Christmas party leader Mike Nesbitt called for Mrs Foster to step down as first minister over her role in the flawed RHI scheme.
Meanwhile, mediators who helped resolve the north's bitterest parading dispute have met the Secretary of State as part of a bid to restore power-sharing.
The "constructive" talks involved hugely experienced community figures who helped defuse the Ardoyne flash point march which has seen dozens of police officers injured and relations between local residents ruined by sectarian violence.
Jim Roddy has been at the forefront of successful negotiations with the Apprentice Boys loyal order over its demonstrations in Londonderry and last year helped the warring parties in the violent north Belfast impasse reach agreement.
Ardoyne Catholic priest Fr Gary Donegan was another key player in ensuring 2016's march passed off peacefully.
A statement from their Making It Work Group said: "We held a candid and constructive meeting with the Secretary of State today to discuss community issues relevant to the ongoing talks process.
"We have agreed to meet with him again over the course of the next three weeks and wished him, Minister Flanagan and all the parties every success during their deliberations."
