Arlene Foster and Michelle O’Neill have written to the prime minister saying the financial proposal around the deal to restore Stormont is not adequate.
DUP MP Sammy Wilson said funding commitments should have been “nailed down”.
Finance Minister Conor Murphy has expressed concerns about the government’s funding offer.
He also said he was trying to “rescue” money pledged in the DUP-Conservatives confidence-and-supply deal.
Mr Murphy is expected to meet the Treasury next week.
Mr Murphy said the letter from the First Minister and Deputy First Minister was sent on Wednesday.
He said it explained that his department is doing a “detailed piece of work” to cost the commitments made in the agreement.
The British and Irish governments have agreed to allocate funding towards the deal, but the exact figure has not been disclosed yet.
It is understood the package from Westminster amounts to about £2bn – but it is not clear how much of that will be extra spending on top of the public money Northern Ireland already receives.
Mr Murphy said he wanted to provide the government with accurate costs for the executive’s priorities.
“We intend to engage with the Treasury, the prime minister’s office and the Northern Ireland Office because that’s where the blockage is,” he said.
“The executive is united in terms of its approach to this.
“Once that work is completed, we will pick that up and we may well be over in London next week talking to people in the Treasury.”
Mr Wilson told BBC Radio Ulster’s Talkback programme that Mr Murphy had “a lot of hard choices to make”.
He said that during the negotiations “the parties put up their wish list but never got any guarantees that there was going to be a lot of extra money available”.
“Julian Smith (Northern Ireland secretary) talked about all of the potential that there was for extra money and the good deal and everything else, but it wasn’t nailed down and now the leverage has gone,” he said.
“I think the other thing is the executive have to be realistic as well that the government is balancing the desires of all the different parties and different MPs here at Westminster.”
He added: “Everybody put forward their wish list so when they were putting forward their wish list to the secretary of state they ought to have been making sure that if there wasn’t the money available for it, that they have some financial commitment to meeting it.
“Don’t forget the secretary of state was keen to get the deal through at that stage.
“If you are looking for who is responsible, every party that put forward its own wish list should have also been thinking about how is this going to get paid for?”
Earlier this week, Mr Murphy said the government’s offer for extra money as part of the deal to restore Stormont “falls way short” of what was promised.
Prime Minister Boris Johnson said the government had made “huge commitments” as part of the deal.
On Wednesday, Mr Murphy responded to Mr Wilson’s comments by saying the “New Decade, New Approach document was drawn up by the two governments and presented on a take-it-or-leave it basis”.
“Rather than prolonging the three-year collapse of the institutions, the parties rightly restored the power-sharing executive and began negotiations on additional funding,” he said.
“As well as seeking that additional funding, I am also working to rescue promised Confidence and Supply money.”
The confidence and supply arrangement between the DUP and Conservatives, agreed in June 2017, included a proposed extra £1bn in spending for Northern Ireland over two years.
“That arrangement between the DUP and the Conservative party collapsed before the money was spent and the British government is now refusing to guarantee the outstanding sums, including the money for broadband,” Mr Murphy claimed.