Arlene Foster's position as DUP leader remains in doubt after one party MP raised the possibility that the former first minister could step aside until the RHI inquiry has concluded.
Public expressions of support for the DUP leader have been conspicuous by their absence over the weekend, albeit former economy minister Simon Hamilton backed her when asked on the BBC's Politics Show.
The DUP remains the assembly's largest party with 28 seats but Sinn Féin has closed the gap on its unionist rival to just one seat.
High profile DUP names who failed to get re-elected included party chairman Maurice Morrow and former culture minister Nelson McCausland.
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While enterprise minister, the Fermanagh-South Tyrone MLA oversaw the roll-out of the botched Renewable Heat Incentive (RHI), which is forecast to cost the Stormont executive almost £500m over the next 20 years.
The generous green energy scheme sparked a controversy that ultimately led to the collapse of the executive and last week's election.
Mrs Foster has continually refused to accede to Sinn Féin demands that she step aside until a forthcoming public inquiry into RHI is completed. The refusal by republicans to accept the DUP leader's nomination as first minister could prevent the restoration of the devolved institutions within three weeks of last Thursday's election.
But over the weekend DUP MP Gavin Robinson raised the possibility that his leader could potentially agree to step aside as the party’s first minister designate.
Mr Robinson stressed that it would be for Mr Foster alone to decide but he added that his party was keen to make Stormont restored.
"As a party that wants to see devolved government in Northern Ireland succeed we are not going to present impediments to progress,” the East Belfast MP told Stephen Nolan on Radio 5 Live.
"But we are not going to have another party determine who is going to lead our party."
However, Strangford MLA Simon Hamilton said Mrs Foster should not step aside.
When pressed on the matter on the BBC's Sunday Politics, he said the DUP leader had the "full support" of her party and the election result was an "endorsement" of her leadership.
The former economy minister said he wanted Mrs Foster to lead the party into this week's negotiations at Stormont House and for her to be re-appointed as first minister.
"I've known Arlene for many years and she's one of the most capable politicians in Northern Ireland," Mr Hamilton said.
"She has my full support, she has the support of the party, and most importantly she has the support of 225,000 people across Northern Ireland who voted for the DUP, who increased the DUP's mandate."
However, Sinn Féin has again insisted that it will not form an executive with the DUP if Mrs Foster is nominated as first minister ahead of the RHI inquiry concluding.
Former education minister John O'Dowd said his party was "not dictating who leads the DUP".
"If the DUP decides, after the implementation talks that are going to take place over the next number of weeks, that they are going to nominate Arlene Foster as joint first minister, Sinn Féin will not support that nomination," he said.
