All efforts must be made to find an alternative to fresh Stormont elections, Irish Foreign Affairs Minister Simon Coveney has said.
Mr Coveney was in Belfast where he held meetings with Sinn Fein, the Alliance Party, the Ulster Unionists and the SDLP.
The DUP is blocking the functioning of the powersharing institutions in Belfast as part of its protest against the Northern Ireland Protocol that has created barriers on the movement of goods between Great Britain and Northern Ireland.
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The UK Government has vowed to secure changes to the protocol, either by way of a negotiated compromise with the EU or through proposed domestic legislation that would empower ministers to scrap the arrangements without the approval of Brussels.
Relations between the UK and EU appear to have improved since Liz Truss became Prime Minister and London and Brussels have been talking up the potential for a deal through fresh negotiations.
Current legislation says that unless Stormont is restored by October 28, Northern Ireland Secretary Chris Heaton-Harris has to call fresh Assembly elections, something he has said he is prepared to do.
Mr Coveney has said that a deal between the UK and EU before October 28 is "not realistic".
He added: "I'm speaking to the Secretary of State on quite a regular basis and we are going to be working together quite intensively over the next few weeks to try to create the conditions to allow all parties in Northern Ireland to believe that they can move back into the space to establish an executive and a functioning Assembly.
"We are looking for a breakthrough on some of these issues in the next few weeks so that we can have the basis for a step forward on some of the contentious issues before the end of October.
"In doing so provide the momentum and encouragement for the one party not willing to re-enter the executive for now, it is worth taking that jump.
"It is time to agree common ground so we can put issues to bed."
Speaking following her meeting with Mr Coveney, Alliance Party leader Naomi Long said: "I am extremely concerned that we are 16 days away from having absolutely no political leadership, political oversight and scrutiny, decision making or direction setting within government.
"We are potentially entering into that void at a time of unprecedented crisis. Not just for individual families through the cost-of-living crisis, but for businesses and the economy through the cost-of-doing-business crisis.
"We saw yesterday, for the first time, a downturn in employment and the impact that will have on individual people's lives.
"And yet it seems that despite all of that, the DUP are willing to use the pain of the people of Northern Ireland as leverage on the protocol."
Sinn Fein vice president Michelle O'Neill said it was not acceptable that an executive at Stormont has not been formed.
She added: "There is one party which is blocking that.
"We need the DUP to join with the rest of us, we need to be around the executive table, we need to be taking decisions in the best interests of people.
"We need to be a strong voice against what is happening in Britain, the fact that mortgage interest rates are going through the roof and affecting pensions.
"It is ridiculous that we don't have a government in place."
But DUP leader Sir Jeffrey Donaldson has said that any agreement over the protocol must produce an outcome which is acceptable to unionists.
He said: "Whether Northern Ireland's place in the United Kingdom is restored by a negotiated outcome or by Parliament legislating is a matter for the Government.
"We hope the negotiations can produce an outcome which is acceptable to unionists, but we are mindful that we tried working devolution for two years and negotiating at the same time only for Brussels to rebuff any progress in that period.
"I note the Prime Minister's commitment today to find an outcome in talks which replicates the Northern Ireland Protocol Bill.
"The Government must recognise that the checks are but a symptom that Northern Ireland is subject to a different set of laws imposed upon us by a foreign entity without any say or vote by any elected representative of the people of Northern Ireland.
"We set seven tests last year. That is the yardstick we will use to measure any proposed solution.
"Devolution can have a stable and enduring future, but it must be built on solid foundations. Powersharing without unionist support is doomed to failure."
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