Scottish Water should be privatised following the resignation of its chairman, according to the Tories.
The executive has provided £2.1bn to improve supplies
Deputy party leader Murdo Fraser said Professor Alan Alexander's decision to step down last week signalled the need for change.
The call was made during an SNP-led debate at Holyrood on the utility, urging clarification on its programme of improvements.
Earlier, the chamber was evacuated after a beam became loose.
Prof Alexander quit as chair of Scottish Water after a plan on delivering improvements up until 2010 was dismissed by ministers and industry regulators.
The Scottish Executive has provided £2.1bn to improve Scotland's water supplies and sewage system over the next four years.
Mr Fraser said he was sure ministers would find "some other mug" to take up the post, but said the utility should be opened up to the market.
He said a private model would remove problems such as infrastructure development constraints, hampering economic growth and social development across the country.
"It is time to take Scottish Water out of the public sector and privatise it," he told MSPs.
"Scottish Water now has to appoint a new chairman. It's difficult to imagine that there would be a long queue of applicants for that job, given the particular difficulties the organisation has faced in the past.
"Whoever comes in will be hampered by the public sector status of the organisation, the constraints upon it and will face the interference of ministers."
Mr Fraser added: "It was too much for Alan Alexander to cope with and he walked away from the job.
"I'm sure that the executive will find some other mug to take on the position but that will not solve the fundamental problem."
Scottish National Party Highland and Islands MSP Rob Gibson, who led Thursday's debate, said the Tories' comparison of Scottish Water with private firms in England and Wales was a "very poor" one.
He said the scale of work Scottish Water had been ordered to complete in eight years had been done over 15 to 20 years by firms south of the border.
Environment Minister Ross Finnie said any delay in the delivery of the investment plan was "something which is to be avoided as far as possible".
He conceded that things had gone "awry" between the time of Mr McConnell's comments and Prof Alexander's resignation but defended the procedures followed throughout.
"In December it certainly was not my wish, nor was it that of the first minister's, that we would get to a point where Scottish Water were unable to meet the requirements of the regulator.
"We had no indication early in December that was going to be the case."
The minister said it was not in the public interest to have a water company seeking to deviate from a determination by the economic regulator.
Labour's Scott Barrie spoke out against the Conservatives' calls for privatisation.
The Dunfermline West MSP said: "I do reject the Tory calls yet again for a privatised Scottish Water.
"I also reject their implicit attack on Scottish Water workers, who provide an essential service sometimes in the most appalling, unpleasant and unsanitary conditions."
Green MSP Eleanor Scott said many issues facing Scotland's water had to be tackled and warned against falling standards.
First Minister's Question Time was postponed after a 12ft-long wooden beam broke free in the chamber.
Deputy Presiding Officer Murray Tosh interrupted speeches to say he had been advised to clear members from the floor area beneath.