DUP leader Arlene Foster says she is hopeful a new budget will be in place for Northern Ireland “within weeks”.
Mrs Foster made the comments after meeting with the prime minister on Wednesday.
Theresa May has been hosting separate meetings with both parties a week after talks aimed at ending 13 months of stalemate at Stormont collapsed.
Mrs May has emphasised that her government remains committed to doing all it can to restore devolution.
Addressing the press outside Westminster, Arlene Foster said: “The people of Northern Ireland deserve to have a budget in place as soon as possible.”
Her party colleague, MP Nigel Dodds added that the party “want to see devolved government” reinstated.
“In the absence of the devolution that we all want, we can’t continue to have Northern Ireland left in limbo as it has been in the last 13 months,” he said.
“We simply want a commonsense interim position, whereby ministers are taking decisions, budgets are being set, whilst we continue to work through the issues.”
In relation to the draft agreement which was leaked on Tuesday, Arlene Foster said it contained “only one of a number of documents that were circulated and put out and about”.
She added that her party was not contemplating introducing an Irish language act in Northern Ireland.
Sinn Féin to meet PM
Representatives from Sinn Féin were also set to meet Mrs May on Wednesday afternoon, and were expected to tell her they would oppose any form of direct rule.
They were also expected to call for the establishment of the British-Irish Intergovernmental Conference, which promotes co-operation on matters of mutual interest between the British and Irish governments.
On Tuesday, Northern Ireland Secretary Karen Bradley declined to immediately re-impose direct rule from Westminster.
Sinn Féin and the DUP – Northern Ireland’s two main parties – had been in negotiations to end a 13-month stalemate at Stormont.
The devolved government collapsed in a row over a botched green energy scheme.
Talks between the DUP and Sinn Féin collapsed last week, and the two sides blamed each other for an impasse over a proposed Irish language act.
The parties still disagree on whether or not a draft agreement was on the table before the talks broke down.
On Tuesday, parts of the draft agreement being worked on were leaked and published.
These confirmed what had already been reported about a three-stranded approach to the language question – which would have resulted in an Irish language act, an Ulster Scots act, and a so-called respecting language and diversity act.
But there was a degree of ambiguity as to whether this had been fully signed off by all the parties.
Meanwhile, on Wednesday morning, MPs on the Northern Ireland Affairs committee took evidence on the issue of devolution.
They heard from witnesses including SDLP leader Colum Eastwood and loyalist blogger Jamie Bryson.