DUP leader Arlene Foster has urged the Northern Ireland Secretary to set a budget and take key decisions about the region’s schools, hospitals and infrastructure.
Mrs Foster made her comments in a telephone call with Karen Bradley on Monday.
Meanwhile, Sinn Féin leader Mary Lou McDonald has again warned direct rule is not an option for Northern Ireland.
Speaking after a meeting with Taoiseach (Irish prime minister) Leo Varadkar and Tánaiste (Irish deputy prime minister) Simon Coveney in Dublin, Ms McDonald called for decisive action from the British and Irish governments.
Following the meeting, the prime minister and Mr Varadkar spoke by telephone.
A Downing Street spokesperson said Theresa May and Mr Varadkar talked about “the recent phase of political talks in Northern Ireland and of their disappointment that an agreement had not yet been reached to restore an executive”.
“Both leaders recognised the progress and serious engagement made by the parties,” the statement added.
“The prime minister said she believed there was scope for agreement and reiterated the UK government’s priority was still to get devolution up and running again in Northern Ireland.”
Mr Varadkar said he emphasised the Irish government’s “full commitment to the Good Friday Agreement, and its determination to secure the effective operation of all its institutions”.
“As co-guarantor to the agreement, the government will continue to engage with the parties in Northern Ireland and the British government to support the urgent formation of a new executive by the mandated political parties,” Mr Varadkar said in a statement.
“The government’s firm position is that the Good Friday Agreement and subsequent agreements must be implemented in full, and in this context the Taoiseach and Tánaiste re-iterated that the Irish government does not want to see the introduction of direct rule in Northern Ireland.”
Mrs Foster said “frontline staff” had been living “hand-to-mouth” for too long and that Northern Ireland’s people deserved better.
“School principals, hospital managers and infrastructure planners have been in limbo for months unsure of budgets and unable to get ministerial direction,” she said.
“I am not prepared to allow this to continue.”
Mrs Foster said she would be raising the issue again at Westminster on Tuesday and would also be meeting the prime minister later this week, where she would “affirm our commitment to devolution but not at any price”.
Both Sinn Féin and the DUP had engaged in negotiations in a bid to end a 13-month impasse at Stormont.
Sinn Féin is also expected to meet Theresa May in London later in the week.
Ms McDonald has said the party still believes a restoration of devolution is possible and said the two governments should urgently convene the British-Irish Intergovernmental Conference to avoid a prolonged stalemate.
“We don’t accept any call for a cooling off period, in fact we’re saying very clearly that there cannot be a vacuum, we need action and we need the two governments to be decisive at this point,” she said.
“Direct rule is not acceptable. Direct rule is not on the table.”
Ms McDonald also appealed to the DUP to return to the talks.
Earlier on Monday, Mr Coveney said direct rule from London would not be acceptable to anyone in Northern Ireland because “people wanted their own government and their own decision-making”.
Sinn Féin has accused the DUP of collapsing the talks and party leader Ms McDonald has claimed a draft deal was in place earlier this month, which included an Irish language act, an Ulster Scots act and a respecting language and diversity act.
Ms McDonald has said talks failed due to disagreements with Sinn Féin about legislation for the Irish language.
Mrs Foster has previously said no draft agreement was in place.
“I regret that we didn’t reach an agreement because they were insisting on having this free-standing Irish language act,” she said.