MLAs met during a recalled sitting of the Assembly on Thursday, but a bid to elect a new speaker did not proceed as the DUP refused to support the nominations.
Stormont ministers, who have been operating in shadow form since the Assembly collapsed earlier this year, will also cease to hold office at midnight.
With time running out ahead of the deadline, Prime Minister Rishi Sunak also urged the DUP to get back to Stormont.
His official spokesman said: “There’s still time for the DUP and executives to get back to Stormont and we urge them to do so because the people of Northern Ireland deserve a fully functioning and locally elected executive, which can respond to the issues facing the communities there.”
The DUP has refused to engage with the devolved institutions in Belfast in the wake of May’s Assembly election, meaning it has not been possible to form an executive.
The party’s boycott is part of a campaign of opposition to Brexit’s Northern Ireland Protocol, and the DUP says it will not return to powersharing until decisive action is taken to remove the protocol’s economic barriers on trade between Great Britain and Northern Ireland.
The Government has vowed to secure changes to the protocol, either by a negotiated compromise with the EU or through proposed domestic legislation – the Northern Ireland Protocol Bill – which would empower ministers to scrap the arrangements without the approval of Brussels.
During the recalled Stormont sitting, the SDLP nominated Patsy McGlone, and the UUP nominated Mike Nesbitt for the position of speaker, which must be filled before an executive can be formed.
However, the nominations failed to secure the necessary cross-community support from MLAs and the plenary session was then suspended as business cannot be carried out without a speaker.
DUP leader Sir Jeffrey Donaldson said his party did not nominate ministers because not enough progress has been made on addressing issues of concern around the protocol.
He said: “We were given a clear mandate in the Assembly elections, and we would not nominate ministers to an executive until decisive action is taken on the protocol to remove the barriers to trade within our own country and to restore our place within the United Kingdom internal market.”
He also warned unionists would not accept a joint authority arrangement between the British and Irish governments instead of direct rule from London in the absence of the Stormont Assembly.
“Joint authority would be an abandonment of the Good Friday Agreement and if that’s what the Irish government want to do, then let them be honest and say,” he said.
Speaking in the chamber, Sinn Fein Stormont leader Michelle O’Neill said the DUP “have left us all at the mercy of a heartless and dysfunctional Tory government”.
Ms O’Neill claimed those watching the proceedings in the Northern Ireland Assembly would be “bewildered”.
“Most of us here want to do the job we were elected to do,” she said.
“Today our caretaker ministers rally to take decisions, within tight limits, before their civil servants are left in an impossible position come midnight where they are expected to run our essential public services yet have no budget and no powers.”
Alliance leader Naomi Long said the people of Northern Ireland were suffering without devolved government, describing public services as “on their knees” or “teetering on the brink”.
The SDLP’s Matthew O’Toole told MLAs he was “ashamed of this place”.