The botched scheme could end up costing the taxpayer up to £400m over 20 years.
Mr McGuinness said it was clear that the RHI scheme had resulted in an "enormous financial scandal".
But, he said his party would not pull the plug on Stormont.
He also called the day's business in the assembly a "shambles" after a vote of no confidence in First Minister Arlene Foster was voted down.
Some 39 MLAs voted for the motion, but it needed 'cross-community support' to pass.
"From my perspective there is an urgent need to restore credibility in the institutions," Mr McGuinness said.
"It is very, very important that the highest level of government - i.e the executive office, that we find a way forward to resolve the quite clear difficulties that are there."
Mr McGuinness suggested that an independent investigation and a credible working relationship between Economy Minister Simon Hamilton and Finance Minister Máirtín Ó Muilleoir could help to cut back on that figure of £400m.
He also called again for Mrs Foster to stand aside while an investigation takes place.
"In my conversation with Arlene Foster a number of days ago I outlined, not an instruction, but what I would do if I were in her position," he told BBC News NI.
"Number one is accept a robust investigation and number two is step down for, what I believe, would be a short period."
On a separate matter, Mr McGuinness commented briefly on his health.
"I am being attended to by a wonderful group of doctors and nurses from our health service and I think that's all I have to say about it at the moment," he said.
The Deputy First Minister Martin McGuiness has told the BBC that Sinn Féin will put forward a motion calling for an investigation into the Renewable Heating Incentive (RHI) when the assembly meets again in January.