The absence of devolved government in Northern Ireland “cannot continue for much longer,” Secretary of State James Brokenshire has said.
He spoke after another day of talks between the Democratic Unionist Party (DUP) and Sinn Féin ended with no deal.
Theresa May phoned DUP leader Arlene Foster and Sinn Féin’s northern leader, Michelle O’Neill on Friday evening.
The PM told them her government was committed to doing all it could to help parties reach a successful conclusion.
‘Running the show’
A No 10 spokesperson said Mrs Foster and Mrs O’Neill “both agreed on the need for the executive to be restored for the benefit of everyone in Northern Ireland”.
“The Prime Minister recognised that constructive discussions had taken place between the parties and urged them both to come together reach a collective agreement so that devolved government could be restored in Northern Ireland.”
The BBC understands the latest round of Stormont talks ended at about 19:30 BST on Friday, breaking up fairly abruptly and not in a positive mood.
Sinn Féin said no progress was made but added talks will resume on Saturday.
Speaking on the BBC’s Any Questions programme, Mr Brokenshire said: “We’ve obviously had an extended period where Northern Ireland has not had politicians making decisions.
“The Northern Ireland Civil Service has effectively been running the show here. That cannot continue for an extended period, for much longer.
“I’ve already had to make certain statements over the budget to ensure that civil servants are able to do their job, so yes, it is about that focus on what now needs to happen.”
When the parties missed a government deadline on Thursday, the secretary of state extended the talks over the weekend, in the hope that a deal will be struck by Monday, when he is due to make a statement on Stormont’s future.
Earlier, Sinn Féin called for the British and Irish prime ministers to become directly involved in the talks process.
The party said the DUP had not moved on a number of issues, including an Irish language act, same-sex marriage, a Bill of Rights and measures to deal with the legacy of the Troubles.
Sinn Féin’s Conor Murphy said it was a “source of frustration” there had been no closing of the gap between the parties throughout the day.
He claimed that the DUP “haven’t yet accepted what brought down the institutions in the first place”.
But the DUP’s Christopher Stalford said Sinn Féin had presented a “shopping list” of demands and was refusing to go back into government until they had received every item on their list.
‘5% budget cut’
His party colleague, Edwin Poots, rejected a call for the prime ministers to get involved and said Sinn Féin knows what is required and “don’t need anyone to hold their hands”.
Mr Poots said Thursday’s missed deadline meant Stormont was now “operating on a 95% budget, which is essentially a 5% cut across all of the departments”.
The DUP MLA described this as “far greater austerity than any Conservative ever imposed upon the Northern Ireland public”.
“Whilst we understand that Irish language is hugely important to Sinn Féin – health, education, jobs, the economy, infrastructure, environment, agriculture – all of these issues are hugely important to us, hugely important to the public,” Mr Poots said.
Responding to his remarks, Mr Murphy said: “The DUP are in absolutely no position to lecture anyone in relation to the provision of public services.”
The Sinn Féin MLA accused DUP MPs of voting for a measure in the Queen’s Speech “which will effectively remove and reduce public sector wages”.
Earlier, his Sinn Féin colleague John O’Dowd said there must be a “step change” for talks to succeed.
“As co-guarantor of the agreements, it is time for the British Prime Minister Theresa May and the Taoiseach (Irish Prime Minister) Leo Varadkar to take direct responsibility.”
Mr O’Dowd also said the DUP’s “confidence and supply” deal with the Conservatives had “emboldened and entrenched” their views, making the prospect of a deal less likely.
A Downing Street spokesperson said that the secretary of state was on the ground in Belfast and would continue to engage intensively with the parties on Friday and over the weekend.
“The prime minister has met with all five parties and will continue to have close engagement with the Northern Ireland secretary and the taoiseach, who she spoke with earlier this weekend,” they added.
‘Crisis to crisis’
The secretary of state has the option of giving the parties more time to negotiate, calling another assembly election or reintroducing direct rule from Westminster.
The independent chair of the talks process, Sir Malcolm McKibbin, formally retired on Friday as head of the Northern Ireland Civil Service.
However, parties asked him to stay on as chair to steer the negotiations.
Analysis: Mark Devenport, BBC News NI political editor
While we’ve bust through another deadline, it’s a deadline that theoretically still exists.
So, Secretary of State James Brokenshire is under responsibility to set a date for a fresh assembly election.
However, everybody is expecting he will consider his options and come through with an emergency law to either allow for yet another deadline or move towards to some form of direct rule.
The mood music around Stormont hasn’t been particularly favourable.
I don’t get any kind of immediate sense that the parties are going to come up with an ingenious compromise.
Under the deal signed in Downing Street on Monday, the minority Conservative government can rely on the support of the DUP’s 10 MPs to get legislation through the House of Commons.
Critics of the deal have questioned whether the Westminster government can act with impartiality between unionists and Irish nationalists when it is dependent on the support of the DUP.
Conservative MP Laurence Robertson told the BBC’s The View programme that Mr Brokenshire would “weigh it up over the weekend” but added he did not believe there was any appetite for another snap assembly election.
Mr Robertson chaired Westminster’s Northern Ireland Affairs Committee for two terms from 2010 until the Dissolution of Parliament in May this year.
He told the programme that Stormont could not “keep stumbling from crisis to crisis” but added he hoped Northern Ireland was not heading for a prolonged period of direct rule.
“I sincerely hope not, I was a shadow minister when we had the last period of direct rule and very important issues are decided upstairs in the House of Commons, in a committee of 20 MPs.
“That’s no way to run Northern Ireland so I sincerely hope not.
“But, somebody has to run the province, so if that’s what Sinn Féin are forcing, well, that might be the only option.”
However, Mr Robertson said he did not think his party’s agreement with the DUP was causing the problem, because Stormont’s latest crisis had happened “long before” the deal.
“I think it’s a problem within Sinn Féin,” the Tory MP said.
“I don’t know what game they are playing, but I do know it’s a dangerous one.”
Northern Ireland has effectively been without a devolved government for almost six months.
Its institutions collapsed amid a bitter row between the DUP and Sinn Féin about a botched green energy scheme.
The late deputy first minister, Martin McGuinness, stood down in protest over the DUP’s handling of an investigation into the scandal, in a move that triggered a snap election in March.