The party has accused SNP ministers of "abandoning" the sector and risking thousands of jobs in the north east.
It comes after the firm behind the controversial Cambo oil field off Shetland announced it was "pausing" the project.
Siccar Point Energy said it was evaluating its next steps, but added: "We continue to believe Cambo is a robust project that can play an important part of the UK's energy security, providing homegrown energy supply and reducing carbon intensive imports, whilst supporting a just transition."
Its decision came just days after Shell, which has a 30 per cent stake in the development, pulled out.
Nicola Sturgeon previously said the Cambo project “shouldn’t get the green light”.
But in an article in the Press and Journal yesterday, the First Minister stressed: "The need to reduce reliance on fossil fuels in a way that is fair and just is critical."
She added: "Let me be crystal clear about my commitment to supporting the industry make the transition that is needed and to securing jobs in the region for the long-term.
"My government is focused on achieving the fastest possible just transition for the oil and gas sector – one that delivers jobs and ensures our energy security, as well as meeting our climate obligations.
"We will not allow the mistakes of the past to be repeated. Indeed, far from deserting the sector, we are already investing in its net zero transformation."
The Tories have accused the Greens, who have two ministers in the Scottish Government following a cooperation agreement with the SNP, of having a “corrosive influence”.
The party’s debate on oil and gas production will take place on Wednesday. Its motion will be defeated as the SNP and Greens have a majority.
Tory MSP Liam Kerr said: “It beggars belief that the SNP are willing to abandon an industry that supports tens of thousands of jobs and adds billions to our economy, simply to appease a few Scottish Green ministers in their Cabinet.
“The corrosive influence of the Greens in parliament is already costing Scottish jobs, and may well have cost us the entire Cambo project.
“This is not the ‘just transition’ that oil and gas workers were promised, this is a sudden cliff edge that risks devastating communities in the North East.
“Imported oil and gas has a carbon footprint more than twice that of domestic production, and would make it even harder for us to reach net zero.
“The SNP-Green Government’s naïve understanding of our energy needs will only force Scotland to import more energy from abroad, costing the public more and increasing emissions.
“The Scottish Conservatives believe that our oil and gas industry has a crucial role to play in our journey to net zero.
"The SNP’s decision to abandon the oil and gas industry in Scotland could destroy Scottish livelihoods for no environmental gain whatsoever – and the Scottish Conservatives are determined to hold the Scottish Government to account on this deeply unjust move.”