The Tories are asking the parliamentary standards commissioner to investigate claims that the first minister leaked information about Scottish Opera.
Scottish Opera staged Wagner's Ring Cycle last year
Brian Monteith said the party would be sending a letter to Dr Jim Dyer on Monday asking him to establish whether Jack McConnell breached the code of conduct.
The row follows a newspaper story which claimed that Scottish Opera would be bailed out to the tune of £5m.
Mr McConnell has denied leaking confidential information.
He has also described calls for an inquiry into the allegations as "ridiculous".
The article which sparked the row appeared in the Sunday Herald last weekend.
Scottish Opera's chairman, Christopher Barron, sent a letter to staff in which he deplored the publication of details of the rescue plan in the newspaper.
He claimed that Mr McConnell was "clearly involved" in a direct leak from the Scottish Executive.
The issue was raised by the Tories and the Scottish National Party at First Minister's Questions on Thursday.
Mr McConnell said he had no intention of ordering a leak inquiry and that everything published by the Sunday Herald had already been in other newspapers.
On Sunday, the Tories confirmed that they would be writing to the standards commissioner over the issue.
Mr Monteith said: "We will explore every opportunity that will force the first minister to answer one
simple and reasonable question, namely did he or anyone in his team give confidential information to the Sunday Herald that was not already in the public domain?"
The SNP's chief whip, Bruce Crawford said a full inquiry was needed to "lift the lid on the nature and culture of the McConnell government".
He said he had "no doubt" that the first minister leaked the information about Scottish Opera.
"The first minister has blown apart his own integrity and honesty and with it he has blown apart his own ministerial code, which he is supposed to be following," he claimed.
"It's time for Jack to do some straight talking instead of continuing to hide behind his spin machine."
Culture Minister Frank McAveety said that the information which appeared in the Sunday Herald was already in the public domain.
He said the "core issue" was that a long-term, sustainable solution had to be found at Scottish Opera.
Jack McConnell has ruled out a leak inquiry
"What we have been trying to do over the past few months is try to arrive at that long-term solution," he said.
Liberal Democrat MSP Donald Gorrie said that the culture commission unveiled by the executive last month needed to get a "real grip" on the funding and organisation of the arts.
"If this commission really stirs up the whole pot it will be worthwhile," he said.
"If it is just another review, when we have had endless reviews, it will be a complete fiasco.
"It has got to deliver a really root-and-branch reform of the whole arts system."