DUP MP Sammy Wilson has criticised James Brokenshire for a lack of clarity about how money secured for Northern Ireland through a DUP deal with the Conservatives can be spent.
Last month, the DUP negotiated an extra £1bn in spending in exchange for backing the Tories at Westminster.
On Wednesday, Mr Brokenshire stopped short of ruling out that it could be dependent on restoring devolution.
The DUP has always insisted the money is not subject to that condition.
Mr Wilson accused the secretary of state of not being able to "give a straight answer", and said it had been made clear to his party that the money was available to Northern Ireland as long as the DUP support the government on certain measures at Westminster.
Under the 'confidence and supply' arrangement the two parties reached last month, the DUP guarantees that its 10 MPs will vote with the government on the Queen's Speech, the Budget, and legislation relating to Brexit and national security.
"As long as we do that, the money is there," said the East Antrim MP, adding that Mr Brokenshire was "pussyfooting around" on the issue.
"If the assembly isn't up and running, then assembly members will not have a decision on how it is spent, it will be direct rule ministers," he added.
"I'd prefer the assembly would have input but if that's not going to happen then why can't he just say it rather than trying to speak on both sides of his mouth?"
The East Antrim MP said the secretary of state needed to make his position clear and said if direct rule is implemented, the DUP will be in a "major position for consultation then" about how the extra funding is spent.
On Wednesday, the secretary of state allocated an extra £131m to health and education in Northern Ireland, as part of a reallocation of funds known as a monitoring round.
It was his second intervention in Stormont's finances in the absence of a functioning executive.
Speaking to BBC Newsline, Mr Brokenshire said the latest funding allocation was not a long-term solution.
"What we're saying is that this money is for a new executive to see that we get local politicians making decisions, there will be a whole host of decisions to take should that not happen," he said.
"I recognise the specific financial needs Northern Ireland has, but the point is that things like infrastructure, roads, investment in hospitals - that requires political decision-making and that why we need to see the parties coming back together again and getting an executive in place."
Asked if the money would be available if there is no restoration of power-sharing at Stormont by 2018, Mr Brokenshire said he would not "hypothesise or speculate" as to what would happen.
The region has been without a functioning executive since January, when the coalition led by the DUP and Sinn Féin collapsed over a green energy scandal.
Talks in both the spring and summer aimed at restoring power-sharing at Stormont failed, with the parties remaining deadlocked over a number of issues.