The Ulster Unionists have rejected DUP economy minister Simon Hamilton's proposal to commission a public inquiry into the renewable heating scandal, claiming there is a conflict of interest.
It comes after Mr Hamilton's special adviser stepped aside from any involvement in the Renewable Heat Incentive (RHI) scheme for failing to declare a family link.
John Robinson's father-in-law receives payment from the scheme for two boilers.
In a statement the DUP said Mr Robinson had no role in his father-in-law's business, but he was stepping aside to avoid the "accusation or perception of a conflict of interest".
Ulster Unionist leader Mike Nesbitt told Mr Hamilton he saw "an insurmountable problem" with him being the minister to commission a public inquiry.
In a letter to the economy minister, he said: "It relates directly and exclusively to the objective of restoring public confidence.
"Section 13 of the Act addresses "Power to Suspend Inquiry", making clear the commissioning minister can stop the progress of the inquiry at any time.
"Given you have prejudiced your impartiality through public statements regarding RHI, such as your repeated assertions the first minister has no case to answer, and further factoring in developments regarding your special adviser, Mr John Robinson, your proposal is not acceptable. You have a clear conflict of interest, on multiple levels."
Mr Robinson is a key member of the DUP's team. He was previously the party's director of communications.
He was accused in the Assembly by former DUP minister Jonathan Bell of interfering in the RHI scheme, but he insisted he had no link to the scheme.
Mr Bell made the allegation on Monday, speaking under parliamentary privilege.
The DUP said the claims were "outrageous".
The Ulster Unionists want the Lord Chief Justice to appoint a judge to lead a public inquiry into the RHI scheme.
Mr Nesbitt said in his letter: "I am sure you and I agree that the 'debacle', to use the first minister's terminology, of the Northern Ireland Renewable Heat Incentive (RHI) has been disastrous for public confidence in the devolved institutions.
"That is why we identified a public inquiry as necessary to start the challenging process of restoring faith in the integrity of Stormont.
"We would have no difficulty with inviting the Lord Chief Justice to appoint the judge who would lead such an inquiry, as we made that suggestion on the day Sinn Fein published their draft terms of reference for an inquiry.
"We pointed out that if restoring public confidence is a key objective, then the Lord Chief Justice, who is not a political appointment, would be better than any attorney general, who is appointed by the first minister and deputy first minister in the Executive Office."
The RHI scheme was set up by former first minister Arlene Foster in 2012 when she was enterprise minister, aiming to increase consumption of heat from renewable sources.
However, businesses received more in subsidies than they paid for fuel, and the scheme became heavily oversubscribed.
It could lead to an overspend of £490 million over the next 20 years.