Boris Johnson has urged political parties in Northern Ireland to step up their efforts to restore devolved government, during talks in Belfast.
The PM held a series of meetings with the five main Stormont parties, in which Brexit was also discussed.
NI has been without a government since January 2017, when the power-sharing DUP/Sinn Féin coalition collapsed.
On Tuesday, Mr Johnson held a private meeting with senior DUP figures, whose support he relies on in Parliament.
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The prime minister left Northern Ireland on Wednesday afternoon and a Downing Street spokesperson said Mr Johnson told the parties while there had been constructive progress in the talks at Stormont, “there now needed to be serious and intense engagement to get this done”.
The spokesperson added that Mr Johnson had told the parties the UK would be leaving the EU on 31 October “come what may” and his intention was to do so with a deal.
In all scenarios, the government was committed to the Good Friday Agreement and in no circumstances would there be physical checks or infrastructure on the border, they said.
Following her meetings with Mr Johnson, DUP leader Arlene Foster said “talk of a border poll” was not something Boris Johnson was “entertaining”.
She met the prime minister along with DUP MPs Nigel Dodds, Emma Little-Pengelly and Gavin Robinson.
Sinn Féin said if a no-deal Brexit happens, the government must call a referendum on Irish unity “immediately”.
But Mrs Foster said the Conservative government would “never be neutral on the union”.
She said discussions regarding the confidence and supply pact the two parties share was for “another day” but defended the £1bn in spending for NI the DUP had secured in the past.
The issue over what will happen at the land border between Northern Ireland and the Republic of Ireland after Brexit – and the proposed Irish backstop – has caused deep divisions between the parties at Stormont.
The backstop is the insurance policy negotiated as part of the UK-EU withdrawal agreement, which aims to keep the border as seamless as it is now and avoid land border checks.
But Mr Johnson has referred to it as a “monstrosity”.
Mr Johnson met Sinn Féin first on Wednesday before talks with the smaller parties and further discussions with the DUP.
After the meeting, Sinn Féin president Mary Lou McDonald said she told the prime minister he must not be “the DUP’s gopher”.
Ms McDonald said she did not believe the PM’s claim he would act with “total impartiality” towards all parties in NI.
“It’s not our business who dines with whom, but the politics of this is the DUP have used this to ensure… the continuing denial of rights and trample on the views of the majority of people who live here,” added Mrs McDonald.
As the talks were taking place, a number of protestors gathered outside, including a group of Harland and Wolff shipyard workers who are lobbying the government to renationalise their workplace.
The Belfast firm’s Norwegian parent company Dolphin Drilling is having serious financial problems and put Harland and Wolff up for sale late last year.
They were joined at Stormont by Irish language campaigners, anti-Brexit protestors and the families of those killed in Ballymurphy in 1971 with others calling for government action on legacy issues.
Northern Ireland has not been ruled directly from Westminster for more than a decade, but it has been without a government since 2017.
Several attempts to kick-start devolution have already failed.
The DUP is due to renew the confidence-and-supply agreement on which Mr Johnson’s Conservative Party depends for a working majority in the House of Commons.
The NI secretary met with the leaders of the five main parties on Wednesday afternoon and has asked the five independent working groups to hold further meetings and report back to him in the coming days.
He said he would then discuss further steps with the Irish government.