DUP leader Jeffrey Donaldson has confirmed that he will not stand down as a Westminster MP "until the Northern Ireland Protocol is resolved".
That means he will not be taking up his seat in the Stormont Assembly.
The Lagan Valley MP made the announcement during a debate in the House of Commons on the Queen's speech.
Under legislation barring double-jobbing, he had a week to decide whether to remain in the House of Commons or take up his seat at Stormont.
Mr Donaldson can co-opt another party member to take his place on an interim basis.
The move clearly signals that he does not expect a return to power-sharing anytime soon.
Meanwhile, Sinn Féin leader in Northern Ireland Michelle O'Neill has said the DUP's refusal to form an executive is punishing the public.
In a post on Twitter, Ms O'Neill said she had spoken to British Prime Minister Boris Johnson this morning, where she told him that people in Northern Ireland cannot be a "pawn" in what she said was the British government's "game of chicken with the EU".
Spoke to Boris Johnson this morning. Reminded him that the DUPs refusal to form an executive is punishing the public, leaving workers & families high and dry. The public here can't be a pawn in the British Governments game of chicken with the EU. Time to form an Executive now.— Michelle O'Neill (@moneillsf) May 10, 2022
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Mr Donaldson spoke to Mr Johnson this morning and said he told him that his party will not nominate any ministers to the Stormont Executive until "decisive action" is taken on the protocol.
The Taoiseach also spoke to the British Prime Minister today, and said they both agreed "on the need to see the NI Executive formed as soon as possible".
Meanwhile, the first meeting of the new Stormont Assembly is due to place at midday on Friday.
Yesterday, Northern Ireland Secretary Brandon Lewis met the leaders of the main political parties, following last week's election, which saw Sinn Féin emerge as Stormont's largest party for the first time.
Following the meetings, he said he had told the party leaders that "our collective focus must be on the restoration of the Stormont institutions so that those newly elected representatives can come together and deliver in the best interests of all the people of Northern Ireland".
SDLP leader Colum Eastwood said it is scandalous that the DUP is still "messing around" and refusing to nominate a Deputy First Minister.
Speaking on RTÉ's Morning Ireland, he also said he considered resigning as party leader following poor election results that saw the party return with eight seats.
However, he said the party asked him to stay on and that is what he will do.
"We're going into opposition and we have a job to do", he said.
Mr Eastwood said more normal politics is needed in Northern Ireland and the SDLP will play its part in that by trying to ensure there is proper accountability in politics.