DUP leader denies party is reluctant to enter a new executive with a Sinn Fein first minister
The UK Government has been urged to focus on resolving issues around the Northern Ireland Protocol rather than calling a fresh Assembly election.
Devolved government in Northern Ireland has been in flux since February when the DUP withdrew ministers in protest against the post-Brexit arrangements.
The six-month deadline for a new executive to be formed following Assembly elections in May passed on Friday, however Secretary of State Chris Heaton-Harris has not yet called a fresh election.
He must do so in the next 12 weeks, according to legislation.
Mr Heaton-Harris is expected to start meetings with the Stormont parties on Tuesday.
DUP leader Sir Jeffrey Donaldson said he wants to see the Stormont Assembly restored as soon as possible, but he does not see a fresh election bringing a solution closer.
He urged that the new few weeks are used to "double down" on getting either a negotiated solution with the EU to issues around the protocol or bringing forward legislation through Parliament.
He told Sky: "We've had three prime ministers, Westminster at times has been in chaos, there's been little focus on getting a solution to the protocol. The talks with the EU only started again a couple of weeks ago, and even then only at a tactical level, not at a political level.
"We tried for over two years to get a solution on the protocol, we worked with the other parties, we pressed the government to take action, and the EU simply said no, there will be no renegotiation of the protocol.
"It reached a point where our ministers in Stormont were required to impose measures on the people of Northern Ireland as a result of the protocol that every single day was harming our economy, our businesses, driving up the cost of living for households.
"I welcome the fact that the EU is now at the negotiating table. Why is that? It's because of the pressure we have put on, it's because of the steps the DUP has taken that finally we're getting a negotiation, a proper negotiation on finding a solution to this problem.
"Let's get on with it, let's get this solution, let's see the negotiations and the tempo of those negotiations increased so that we get to an outcome that unionists can support."
However Sinn Fein Stormont leader Michelle O'Neill said she believes the "real motivation" is that the DUP is not comfortable entering an executive led by her party for the first time.
The election in May saw Sinn Fein overtake the DUP to become the first nationalist party to be the biggest at Stormont. This entitles Sinn Fein to nominate a first minister for the first time.
She told Sky: "I don't think it's lost on the wider public that the DUP don't like the May election result, I don't think it's lost on the wider public that they have difficulty in forming a government to be a deputy first minister to my mandate which is to be the first minister given the recent election results.
"I think it's not lost on people that that's the real motivation here. The DUP hide behind the issues of the protocol.
"What I want to see in the time ahead is very mature, sensible political discussion between both the British Government and the EU side.
"Let's find an agreed way to solve the issues around the protocol, and I would make this case again to disagree with Jeffrey Donaldson and the DUP - the protocol is a necessity and it is here to stay.
"There are things that can be smoothed out, there are things that can be made to work better, and I'm up for that and hope that's what we achieve in the coming weeks and months."
Ms O'Neill also urged for efforts to be ramped up to find an agreed way forward, saying that will provide certainty and stability as well as "remove any pretence by the DUP in terms of forming an executive" with Sinn Fein.
Sir Jeffrey denied his party is reluctant to enter a new executive with a Sinn Fein first minister.
He said he withdrew his ministers in February, before that election outcome in May.
"This is not to do with who is the first or deputy first minister... this is about the union. It is about unionists feeling they have been made second-class citizens as a result of a protocol that diminishes and undermines our place in the United Kingdom," he said.
Ms O'Neill said she does not want to see another election but it is necessary because the result of the last poll in May has not been respected.
She blamed the DUP: "They have failed to accept the outcome of that election, they have failed to form a government, and they failed to work with the rest of us to get people through these times.
"We shouldn't have to have an election... but unfortunately that election result is being disrespected.
"What we have at this current moment in time is six months post that election, we have a state of limbo, we have no government in place, we have no ministers in post, we have nobody taking decisions in the interests of the people and it's just not acceptable. It's just not good enough."