Sir Jeffrey Donaldson has said it is the "government's call" on whether an election is called after the October 28 deadline to restore the Stormont assembly.
Speaking after meeting Taoiseach Micheál Martin, who is in Belfast to hold discussions with Stormont parties ahead of next week's deadline, the DUP leader said: "We want to see the political institutions up and running as quickly as possible.
"But in the current circumstances, it's difficult to see that solution coming forward before the 28th of October, we have to be realistic about that.
"The question as to whether there should be an election is a matter for the Government entirely. We are very clear - if the government decides to call an election, we will fight that election, we will take our case to the people."
He added: "I don't know if the government will call an election on the 28th of October, I am certainly not going to seek to influence that decision, because it is their call at the end of the day, beyond saying this - that having an election won't change the need to sort out the protocol and to get firm foundations for having the political institutions restored here.
"It will not change my view, it will not change the view of the wider unionist community that the protocol needs to be sorted out. So an election won't change that."
The Lagan Valley MP said if another election was called he would be contacting other pro-union parties to see it they could achieve greater cooperation and avoid "divisions and splits" within the unionist vote.
"We will look to the other parties to see what level of cooperation and working together we can achieve to maximise unionist representation," he said.
"I think that the unionist community recognises that divisions, splitting the vote doesn't win elections and doesn't win seats for unionism."
Sir Jeffrey said he felt the Dublin government had recently developed a better understanding of unionist concerns about the Northern Ireland Protocol.
"I think it is clear that the Irish government share our view now that we're not looking here at some kind of a quick fix, that what we need to do is deal with the protocol issues comprehensively, that we need to get to a place where the foundations for the political institutions are restored and strengthened and that's where we want to get to," he said.
Sir Jeffrey said there could be no "tinkering around the edges" with the protocol and there was a need to replace it with arrangements that "respect the integrity of the UK internal market".
"I think the Irish government recognises and understands our position better now than perhaps had been the case in the past," he added.
Sir Jeffrey said he was aware that operations, including heart surgery, were being delayed due to protocol red tape.
"Because our health service couldn't access what they needed, the components for that surgery, from their normal suppliers in Great Britain they had to go to another country," he said.
"And that meant two weeks of delay where people were waiting on vital surgery, life-saving surgery directly as a result of the protocol.
"This is harming people's lives. It's harming people's livelihoods."
Sir Jeffrey also said he had asked the Taoiseach to use his influence to ask people to desist from singing offensive songs which glorify terrorism.
The Irish women's football team apologised last week for singing a pro-IRA chant, and a group of passengers at Dublin Airport were filmed at the weekend singing the same song.
Speaking following a meeting with Mr Martin, Sir Jeffrey said: "We had the singing at the weekend and last week of songs that are deeply offensive to many people, including victims. And I recognise this isn't just a problem on one side.
"But certainly when you have people who are role models in a community or society who are engaging in this in this kind of activity, it doesn't do anything to create the kind of atmosphere that we need to make progress.
"And so we're, we are asking the Irish government to use their influence in their jurisdiction to ensure that, that people desist from this kind of behaviour."
The DUP leader referenced a weekend attack on an Orange Hall in Co Down, saying: "Over the weekend I was visiting a little Orange Hall, that through the whole period of the Troubles, was never once touched, unaffected, good relations in that community.
"That hall is used by all sections of the community, and yet they had their windows smashed.
"There's cause and effect. When people create a bad atmosphere, unfortunately, people do bad things."
After his meeting with the Taoiseach, SDLP leader Colum Eastwood said it was "totally irresponsible" for the DUP to prevent the formation of an executive.
"There's a massive crisis in people's homes right now, there's a crisis as there always is in the health service, and our economy is in the toilet and all the way the DUP are sitting out pretending they're having some influence on the protocol negotiations," he said.
"It's fairly coincidental that the first time they don't come first, they don't go into government. The DUP know well that their absence from Stormont has no impact whatsoever on the negotiations between the European Commission and the British government. If they want to do a deal, there'll be a deal done. It won't be because Jeffrey Donaldson stomps his feet. I have always suspected that the DUP just didn't want to be deputy first minister to a Sinn Fein, or any nationalist frankly, first minister.
"Well, they're going to have to get over that because the people have spoken and the people are demanding their politicians go to work."
Naomi Long said a winter election would be inevitable if the DUP continued to "dig in" ahead of the October 28 deadline.
Speaking after meeting the Taoiseach, the Alliance Party leader said: "If they continue to dig in then it is inevitable.
"But I think the more important question is what purpose does that serve?"
She added: "We cannot keep running elections in Northern Ireland until the main parties are satisfied with the outcome.
"That isn't democracy. We've got our answer from the public, the job of a politician post-election isn't to demand another one, so they can get a better result - it is to work on the basis of the mandate they got to deliver as best they can for the public."
Ulster Unionist leader Doug Beattie said there was a clear “landing zone” on which the UK and EU could agree a compromise deal on the Northern Ireland Protocol.
“We’re now hovering above it and all we have to do is land and that takes courage,” he said.
He said the UK Government should remove the “artificial gun to the head” of the October 28 deadline for calling a fresh Assembly election.
“There is absolutely no point holding a gun to anybody’s head on an election on the 28th of October because the end result on the 8th of December (potential election date) will be exactly the same position we are now, only worse,” he said.
“What I’m saying is simple. Let’s get this across the line. Let’s get the landing zone. Let’s take away the artificial gun to the head of the 28th of October election. Let’s come up with a solution. Let’s come up with a deal. Let’s get back into government now.”
Mr Beattie also ruled out any deal with other unionist parties in the event of an election that would see his party standing down candidates in constituencies.
“The bottom line is, and people need to understand this, you can slice the pie up all you want, but it will still be the same size of pie for unionism,” he said.
“What I want to do is grow the pro-Union vote and you grow the pro-Union vote by reaching out to all of the people and to reach out to all the people you must stand in the elections.”
Sinn Féin vice president Michelle O’Neill has urged people to be respectful of each other following recent incidents where videos of groups singing pro-IRA songs were posted on social media.
Speaking following a meeting with Taoiseach Micheál Martin, Ms O’Neill said: “I think we all should be very sensitive to the needs of victims and survivors and be very mindful of that.
“I think all of us in public life or just in life in general, we should be sensitive to that. I think that we need to be civil, and we need to be respectful in what we say.
“People have said their piece in terms of what happened.
“I can’t police everything that I see appearing on social media, but what I can say is that we should all be respectful of each other.”
Ms O’Neill said Northern Ireland could not be the “collateral damage” from the instability with the current UK government.
“I believe that we shouldn’t be collateral damage to the mess that’s happening in London, I believe that we shouldn’t be held ransom because of what’s happening with the internal wranglings of the Tory party.
“Regardless of all of that, and whatever happens, and what unfolds there, what we need to see is an agreed way forward within the framework of the protocol, find ways to make it work, and get on with that piece of business because that seems to be the blockage, certainly, according to DUP, in terms of forming an executive.
“So there shouldn’t be any more delay and where we need to be today is around an executive table.”
Commenting on the October 28 deadline for calling a new election, Ms O’Neill said: “Next Friday ministers will cease to hold office, Conor Murphy will no longer be the finance minister, all the other ministers cease to hold office. That’s not good enough for the public. They need us around that executive table. And that’s where we all should be.”
She added: “The DUP need to join the rest of us who want to make politics work, who want to honour the election result from May past and who want to actually help people through what is the most challenging of economic times.”
Sinn Féin’s meeting with Taoiseach Micheal Martin came a day after the Fianna Fáil leader accused the party of using legal threats to shut down debate and avoid accountability.
Michelle O’Neill said she did not raise his comments during their encounter in Belfast, describing the meeting as “workwoman and workman-like”.
She said Mr Martin wore “two hats” – Taoiseach and leader of the Fianna Fáil party.
“He’s here as Taoiseach,” she said of the Belfast visit.
“I think it’s important that I keep the focus today on what’s important and that is food on people’s tables, heat in their homes, it’s about getting them through the months ahead, the difficult months ahead, and also then what the Taoiseach can do to ensure that he fulfils his role as co-guarantor (of the Good Friday Agreement).”
