Constitution Secretary Michael Russell made the claim after Tory MSP Adam Tomkins repeated the call for the First Minister to quit when he appeared on the BBC’s Sunday Show.
And Mr Russell also accused the Tories of “turbo-charging” attempts to undermine the Scottish Parliament.
Mr Tomkins told the programme: “The evidence is not just clear but overwhelming that Nicola Sturgeon has misled parliament on countless occasions.
“If you are a minister in the Scottish Government you have to abide by the ministerial code. The ministerial code makes it absolutely clear that if you mislead the Scottish Parliament you resign. She misled the Scottish Parliament and she needs to resign.”
Mr Tomkins also said he was “really worried” about the state of the Scottish Parliament.
He said: “I think the Scottish Parliament is quite a good parliament when it comes to making laws for the people of Scotland, but frankly it's a lousy parliament when it comes to standing up to the executive of the day and holding the executive to account. That's not because the Scottish Parliament lacks powers, it’s because too many people in the Scottish Parliament lack the will to use the powers we have.”
Mr Russell compared the Tories’ approach to the Trump supporters’ chant about his Democrat rival in the 2016 US election, Hillary Clinton.
“What you’ve just heard is a version of the Trump cry ‘Lock her up’ – if you remember that used to be shouted at every Trump rally, that’s what you’ve just heard, and the Tories have been doing it for weeks and it’s thoroughly unpleasant, and it’s focused on an individual, and it’s focused on undermining the Scottish Parliament.“It’s utterly discreditable and the people of Scotland need to have their say about it.”
He said the UK Tory government had been trying to undermine the Scottish Parliament for the past three or four years and that was now being “turbo-charged” by the Scottish Tories.