A deal for the Democratic Unionist Party to prop up the minority Tory government is "all but done" after talks between Theresa May and Arlene Foster, ITV News understands.
Only minor details remain after the leaders held negotiations at Downing Street, ITV News Political Correspondent Carl Dinnen reported.
The DUP head told ITV News she had "some very good discussions" with Mrs May and was hopeful of reaching a conclusion "sooner rather than later".
Mrs Foster would not go into great detail about the talks but said government stability, Brexit, counter-terrorism and doing what's right for Northern Ireland economically were high on the agenda.
Mrs Foster had earlier waved to the press pack as she arrived with colleague Nigel Dodds at Number 10 around 12.50pm, but refused to confirm to reporters whether she would agree to a deal.
It was thought the Brexit-supporting Mrs Foster was seeking assurances from Mrs May that she will pursue a softer exit from the EU as part of her demands.
Speaking after a meeting with French President Emmanuel Macron, Mrs May called the talks with the DUP "productive" and said that they would help "to give the stability to the UK Government that I think is necessary at this time" and "in the national interest".
Mrs May continued that the Government remained "absolutely steadfast" in its commitment to the Good Friday Agreement and devolved power-sharing at Stormont, amid fears a DUP-Tory alliance could put fragile agreements at risk.
She continued that the Tories would "continue to work with all the parties in Northern Ireland and with the Government of the Republic of Ireland in ensuring that we can continue to put in place those measure necessary to fulfil those agreements" and restore the devolved administration.
The DUP's desire is not to see a return to a hard border with Ireland, while Northern Ireland delivered a 56% Remain vote in last year's EU referendum.
Mrs Foster was almost certain to ask for greater investment in Northern Ireland as part of the deal, though changes to security and legacy issues from the Troubles were unlikely to be included in a pact.
Mrs May's largely unchanged Cabinet earlier discussed plans for the scope of negotiations in a meeting that lasted around 90 minutes.
The Prime Minister's spokesperson only confirmed an "update on the on-going talks with the DUP" took place as the ministers gathered once again in the wake of last week's disastrous election.
The mooted "confidence and supply" arrangement with the DUP would see Mrs Foster's party back the government budget and support it on any confidence motions.
Labour leader Jeremy Corbyn has said Labour stands ready to vote down the Queen's Speech, which sets out the government's legislative agenda, underlining the need for Mrs May to secure DUP support from the outset of the new parliament.
On Tuesday Sinn Fein's seven MPs held a briefing in London with reporters after warning the DUP deal undermines power-sharing talks in the gridlocked Northern Ireland executive, a claim rejected by Mrs Foster.
In the briefing they said the prospect of an agreement between the Conservative Party and the DUP was causing "anxiety and fear" over fears that any deal agreed on would affect issues relating to Northern Ireland.
However, some positives could come out of the potential deal, Barry McElduff, the newly elected Sinn Fein MP for West Tyrone said.
"Maybe the people of England, Scotland and Wales will begin to learn about the true nature of the DUP, their homophobia, their sexism, their sectarianism and their anti-Irish regressive, politics.
"So maybe every cloud has a silver lining and maybe people here will begin to understand what they're dealing with, with the DUP."
The party continued that any deal agreed between the two parties could affect the ability to form a new Stormont Government.
Sinn Fein added that taking Northern Ireland out of the European Union also undermined the Good Friday Agreement.
The PM also told the Conservative backbench 1922 Committee on Monday a deal with the DUP would not affect power-sharing at Stormont, nor LGBT rights after public concerns over their new allies' views.
Mrs May's rivals have also warned the government's claimed impartiality as a mediator in the Northern Ireland political dispute would be fatally undermined by the DUP pact.
The Stormont parties have until a June 29 deadline to reach consensus and re-establish a ruling executive.