The people of Northern Ireland would not support any party bringing down Stormont at a time when the Executive faces such urgent issues, Brandon Lewis has warned.

The Northern Ireland Secretary was commenting on the prospect of the DUP following through with its repeated threats to withdraw its ministers from the Executive – a move that would collapse the institutions – if major changes are not secured to Brexit’s Northern Ireland Protocol.

Mr Lewis said he had given the same message to Sinn Fein when it threatened not to participate in the Executive in a row over Irish language legislation in the summer.

At the weekend, DUP leader Sir Jeffrey Donaldson said Prime Minister Boris Johnson’s position of continuing to state that talks with the EU on the protocol were ongoing, but without indicating any sign of significant progress, was “not sustainable”.

He said Mr Johnson had to realise that if there was no progress the DUP could not continue to participate in the political institutions.

Mr Lewis told the PA news agency it was right that the Government gave the negotiation process time.

The protocol, which was agreed as part of the Brexit divorce deal to ensure a free flowing border on the island of Ireland, has created a series of new checks and processes on Irish Sea trade between Great Britain and Northern Ireland.

London and Brussels are trying to reach agreement that would reduce customs paperwork and the numbers of checks and inspections required on goods moving from GB to NI and ensure a continued free flow of medicines across the Irish Sea.

While both sides are understood to have made progress on the medicines issue, with an announcement from the EU anticipated this month, there is no sign of immediate breakthroughs on the other issues of dispute.

“It is in everybody’s interest for us to take the time to work through and find a resolution that is an agreement between us and the EU, I know it’s what the business community want, it’s what the wider community I think wants to see – a resolution that we can all agree because that gives certainty and definition,” said Mr Lewis.

Asked about the DUP threat to withdraw ministers from Stormont, the Secretary of State added: “I’ve been clear all the way through this year to all of the parties who have made different statements over different issues at different times that I don’t believe that people in Northern Ireland want to see anything other than a functioning Stormont, a Stormont that is delivering for people on the local issues that matter.

“When you’ve got a third of the population on the health waiting lists, the population wants to see Stormont dealing with issues like that, actually delivering on things like education. That’s what people want to see.

“And I don’t think anybody’s going to be supportive of any party who’s looking to do anything other than to keep those institutions running. I felt that in the summer, I feel that now.”

Mr Lewis was attending an investment event in Belfast’s Waterfront Hall along with DUP First Minister Paul Givan and Sinn Fein deputy First Minister Michelle O’Neill.

Mr Givan said he anticipated UK Brexit minister Lord Frost to make a statement on the state of the talks process later this week. He said he also expected an EU move on medicines before Christmas.

“We need to make sure that the fundamental building blocks that our Executive are based upon are sustainable, and that requires unionists and nationalists to support those institutions and the protocol has undermined the basis in which the Belfast Agreement (Good Friday Agreement) operates,” he said.

“So I’m always pushing for the best possible outcome. Jeffrey (Sir Jeffrey Donaldson) is working tirelessly to deliver on that. And we need to ensure that we get to that end destination place so that the institutions can continue to operate to tackle all of the issues that are important to the people of Northern Ireland. And I’m committed to getting a successful outcome just as Jeffrey Donaldson is.”

Ms O’Neill said the talks could not go on forever. She also called on the DUP to “step back from the brink”.

“I think we are inching towards progress around the issue of medicines,” she said.

“I think that will be significant in order to set the tone right in terms of what else needs to be resolved.

“So there needs to be solutions found here. And the DUP need to step back from the brink in terms of threating the institutions at a time whenever the rest of us are focused on dealing with the pandemic, dealing with trying to build the economy, dealing with trying to prioritise health in a budget.

“There are huge challenges for us as an Executive and I think the DUP would be better facing inwards towards the rest of the parties instead of sitting as an outlier in terms of what’s in the best interests of people here.”