Theresa May yesterday told Arlene Foster and Michelle O'Neill that the Government will reluctantly bring forward a budget bill on Monday.
In phone calls with the DUP and Sinn Fein, the Prime Minister voiced concern that the talks aimed at restoring devolution had so far failed to reach an agreement.
A No 10 spokeswoman said: "In separate phone calls, she expressed her concern that despite recent progress, an agreement had not yet been reached and she urged both parties to bridge the gaps on the outstanding issues that remained.
"On Northern Ireland's finances, the Prime Minister explained how the UK Government will reluctantly be taking forward legislation for a Budget Bill on Monday, to ensure that in the absence of an Executive, public services in Northern Ireland have the resources they need to operate.
"The Prime Minister made clear this was absolutely not an indication of direct rule but it was necessary to enable the Northern Ireland Civil Service to allocate funds for key public services while talks between the parties continued."
The spokeswoman added that there was agreement on the importance of devolved government being returned to Northern Ireland and said that the UK Government would continue to work alongside the Irish Government, with the parties to try to eventually reach an agreement.
Speaking in Kilkeel last night, the DUP leader Arlene Foster (right) said that any new Executive in Northern Ireland must be restored "on a sustainable basis".
She insisted that her party was determined to secure an agreement that could be supported by both unionists and nationalists, with no group dominating the other.
The party's key role in holding the balance of power at Westminster did not distract it from what it needed to do at Stormont, she said.
It was "not a choice for the DUP between influence in London and Executive power in Belfast".
Mrs Foster maintained that "solid progress" had been made in talks with Sinn Fein, but "in some areas differences do remain and hurdles have yet to be overcome".
She continued: "For our part we are determined to try to achieve an agreement that can be supported by unionists and nationalists.
"If we are to build a society that can move forward sustainably, then we must be able to demonstrate to one another that no one culture can have dominance over the other.
"One element of the talks is that any new Executive must be restored on a sustainable basis and all parties who share that view must insist on that being the case."
Negotiations to restore devolution broke down last week, with the DUP and Sinn Fein both blaming each other for the political stalemate.
Mrs Foster welcomed Secretary of State James Brokenshire moving to pass a budget for Northern Ireland in the House of Commons next week.
"We are strongly arguing the case for a budget that helps business grow and cuts red tape," she said.
She added: "The way to help local people and local business succeed is to provide them with the environment to do business and to invest in infrastructure projects to boost productivity."
Referring to her party's confidence and supply agreement with Theresa May's government, the DUP leader said that she was in London on Tuesday for a meeting of the co-ordination committee between her party and the Tories.
"The new political realities mean that in order to secure legislation through the Commons, the Government works with our 10 members on a range of issues including Brexit and budget-related bills.
"We are keeping Northern Ireland's interests to the fore," she added.
Speaking after the call, Gerry Adams, who is in New York with Michelle O'Neill and Mary Lou McDonald, said: "Sinn Fein was flexible and willing to stretch ourselves in an effort to achieve a breakthrough.
"However, despite our best endeavours the discussions were unsuccessful.
"I told the Prime Minister May today that the British Government must bear the greater responsibility for this failure.
"The provision of an Irish Language Act, Marriage Equality, a Bill of Rights and funding for legacy inquests are all British government obligations."
Mr Adams said that he had also told the PM that "direct rule was not an option" and she should establish an intergovernmental conference involving the Irish and British governments.
He said: "In the absence of the institutions the two governments must implement those outstanding rights issues.
"Sinn Fein remains committed to the restoration of the institutions and the Executive.
"However, they will only be credible if they are sustainable and durable and deliver for everyone."