Martin McGuinness has said Arlene Foster should stand aside as First Minister while the Renewable Heating Initiative is investigated.
In response, the DUP said Ms Foster "will not be stepping aside" and added that the First Minister "does not take her instructions from Sinn Féin, but from the electorate".
The deputy First Minister says he spoke to Arlene Foster by phone on Friday afternoon and outlined his "serious concern that the credibility of the political institutions is being undermined by the serious and ongoing allegations" surrounding the scheme.
Mr McGuinness said there should be a "fully independent investigation into this matter".
A statement from the Sinn Féin politician continued: "This scheme has directly impacted on the public purse.
"Taxpayers’ money wasted in this scheme, needs to be retrieved.
“It is my belief the only way to establish the truth, and rebuild the reputation of the institutions, is to urgently establish a fully independent investigation into this matter.
“In addition, I also said that, in the public interest, she should stand aside from the role as First Minister while that investigation is underway and at least until an initial assessment had been concluded into the veracity of all the allegations.
“That is what I would do if I was in this situation. I asked the First Minister to take the time and consider this suggestion carefully.”