DUP leader Sir Jeffrey Donaldson has said he cannot set out a timetable for his party to return to Stormont power-sharing.
He said they needed to see how the incoming Prime Minister succeeding Boris Johnson will respond to unionist concerns over Brexit's Northern Ireland Protocol.
Sir Jeffrey was speaking ahead of latest attempt to restore the political institutions in Northern Ireland through a recalled sitting of the Assembly on Wednesday.
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The move by the SDLP is set to fail as the DUP has made clear it will continue to block the election of a Speaker, meaning no further business can be done.
Stormont has been in limbo since February when the DUP withdrew its First Minister from the Executive as it called for the UK government to act on the protocol.
The DUP has linked its return to Stormont with contentious legislation passing through Parliament which aims to override the Irish Sea trade deal agreed with the European Union.
But the Conservative Party leadership contest between Foreign Secretary Liz Truss and former Chancellor Rishi Sunak has led to uncertainty over how the next Prime Minister will proceed with the Bill.
Sir Jeffrey said: “We need to know where that new Prime Minister is going with the Protocol Bill. We need to know is that Prime Minister going to reopen negotiations with the European Union, and what might that mean.
“How quickly are we going to see progress towards the solution that we need on the protocol, because that’s what I need to see happening.
“So can I, right now, look you in the eye and say ‘Here is the timetable’? Of course I can’t because I don’t know at this stage who the Prime Minister is going to be, I don’t know at this stage what line they are going to take."
He added: “The sooner we can get to a solution on the protocol, the sooner we will see the cross-community consensus restored that is necessary to operate the political institutions in Northern Ireland.
“I want to see that happen quickly. That’s why I pushed for the Protocol Bill to be put through the House of Commons in all its stages before the summer recess.
“I would like to see it through in the autumn so that the Bill is in place and the enabling regulations that flow from that Bill can be brought forward and the solution on the ground can be put in place.”
Sir Jeffrey, who dismissed the recall of the Assembly as a “stunt”, declined to say who he would prefer to see as the next leader of the Conservative Party.
“That’s a matter for the Conservative Party,” he told BBC Radio Ulster's Good Morning Ulster programme.
The SDLP, which has assumed the role of official opposition in the Assembly, said the recall session would serve as a challenge to the DUP to "get back to work".
A motion to debate the cost-of-living crisis has also been scheduled for the session, but this will not proceed without the election of a Speaker.
SDLP Stormont leader Matthew O’Toole said it is "outrageously cruel" for the Assembly not to be functioning at a time when families are struggling with rising prices.
He said the inflation crisis has worsened since the last recalled sitting in May and there is also a need to press the DUP on its timetable for re-engaging with Stormont.
“Those are substantive real reasons for us to recall the Assembly and find out where the DUP are, frankly, why they’re continuing to operate this veto,” he said.
“So I completely reject the idea that it is somehow a stunt or that it’s pointless to recall the Assembly."
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