The first minister has denied claims he leaked confidential information about a rescue package for Scottish Opera.
Scottish Opera has had long-standing funding problems
However, the SNP has written to John Elvidge, the executive's permanent secretary asking for a leak inquiry.
The row stemmed from a newspaper story which said the company would be bailed out to the tune of £5m.
A spokeswoman for Mr McConnell admitted he did have an off the record chat with a newspaper editor, but no information breaching ministerial codes was given.
In a letter to staff at Scottish Opera, its chairman Christopher Barron said he deplored the publication in the Sunday Herald which gave details of the rescue.
The newspaper article did not attribute the details to Mr McConnell, although it included general comments from him on the problems of Scottish Opera.
But in his correspondence with employees, Mr Barron said the article covered matters which were only made known to himself and opera board members last Friday.
He said: "The article was the result of a direct leak from the executive in which clearly the first minister has been involved.
"It contains very specific new information which directly affects staff."
The Sunday Herald said a financial bail-out of up to £5m would be used to pay for a root-and-branch overhaul of the company which would see chorus
members go part-time and Scottish Opera give up the running of its Glasgow base, the Theatre Royal.
On Wednesday a spokeswoman for Mr McConnell said: "He (Mr McConnell) is firmly of the view that there was no confidential information passed that would have
caused any breach of the ministerial code."
"The first minister has not, in his opinion, leaked.
"He had an on-the-record interview with a journalist, and he also had a conversation with the editor of that paper."
Decline to comment
"I would expect that some of the information given to the editor might be off-the-record.
"That is not to say that he leaked confidential information."
Nor was she suggesting, she said, that the editor Andrew Jaspan, had broken any confidences.
"I'm not suggesting for a minute that Andrew Jaspan breached any kind of confidentiality," she said.
"All I'm trying to say is there was a conversation between them, as you might expect in this situation."
Scottish Opera has declined to comment on the affair, but confirmed that Mr Barron had sent a letter to staff.
Jack McConnell admitted to an "off-the-record chat"
The Tories have demanded that Mr McConnell explain to parliament how the executive was handling the opera rescue package.
The party's finance spokesman Brian Monteith said: "The first minister has broken what I understood to be a firm agreement between Scottish Opera and the executive that no details would be revealed until talks had been concluded.
"By making public the transfer of the running of the Theatre Royal as part of the rescue plan, he has jeopardised the value that Scottish Opera, and therefore the Scottish taxpayer, might gain from any sale.
"This is a serious breach of commercial confidentiality that calls into question the judgment of the first minister."
Liberal Democrat MSP Donald Gorrie said that "clearly something had gone wrong" but it "wasn't a hanging matter".
Scottish National Party chief whip Bruce Crawford raised the matter in the Scottish Parliament on Wednesday, asking Deputy Presiding Officer Murray Tosh if the executive was making a statement to Holyrood later this week.
He also asked: "If the first minister is responsible for enforcing the ministerial code, who then would undertake any investigation into the question
of whether a breach of the code had occurred or not, given that it's the first minister himself who would be at the centre of any investigation?"
Mr Tosh told him: "On the basis of a request for information, I can say that no such request for a statement has been offered.
"On the matter of the ministerial code, it has been ruled frequently in the past that this is not a matter for me or for any occupant of this chair, but is a matter for the first minister."
Brian Monteith: "Serious breach"
Mr Crawford later wrote to John Elvidge, permanent secretary to the Scottish Executive, asking for a formal leak inquiry.
He said: "The chief executive of Scottish Opera - a man with no political axe to grind - has made a direct accusation that the first minister was involved in this
"Jack McConnell admits that he spoke off the record to a Sunday paper, but claims he has no idea how that self same paper got the Scottish Opera leak. Who
are we to believe?"
He went on: "The first minister has been directly accused of revealing details of the future of people's jobs before they themselves knew there was
even a question mark hanging over them."