With several Holyrood committees due to publish reports on the draft plan on Friday, the Green co-convener urged SNP ministers to do more to ensure it contains the "ambitious choices" that are needed.
The blueprint for tackling global warming was published by the Scottish Government in January.
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Mr Harvie accused the SNP and the other parties at Holyrood of clinging on to a "shared desperate attachment to the economics of the fossil fuel industry".
He pressed Mr Swinney on the issue at First Minister's Questions, where the Deputy First Minister was standing in for Nicola Sturgeon.
Mr Harvie said: "Over recent weeks, parliamentary scrutiny of the Government's draft climate plan has exposed serious omissions and contradictions.
"We've seen the Environment Secretary defending a plan that does nothing to improve bus use and saying car journeys are destined to go up by 25% while the transport minister says 'no, that's only worst-case scenario'.
"We've had the Environment Secretary telling the chamber about a Government policy for compulsory soil-testing to reduce fertiliser use and a fortnight later the Rural Economy Secretary writes to committees to say 'no, that's definitely not happening'.
"Although the Finance Secretary admits that there has been no attempt to build a credible economic case for his plan to cut aviation tax, he tells us that the rest of the economy can make up for the extra emissions from all that flying, even though the climate plan itself is utterly devoid of detail for how that is going to happen. The climate plan is barely half baked.
"Isn't it clear that major changes are needed if we're going to ensure the ambitious choices Scotland needs to make are actually written into the plan?"
The Green MSP added that from the evidence already heard by committees and from the questions that have been asked, "it's very clear that there is serious concern and that changes to this draft plan will need to be equally serious".
Mr Swinney told him the issues he had raised "demonstrates the rigorous scrutiny that is exercised on the Government by parliamentary committees".
The Deputy First Minister added: "The Government's climate change plan takes in a huge number of measures and interventions across government to enable us to fulfil the targets that we have set for ourselves."
Ministers committed to cut harmful CO2 emissions by 80% by 2050, with a new interim target of 50% by 2020 set after the previous goal of a 42% reduction was achieved in 2014, six years early.
Mr Swinney said: "The Government has already achieved early the 2020 target that we put in place for carbon emissions reductions, that's something we should all as a Parliament be proud of.
"We legislated for that ambitious legislation a number of years ago and we're now seeing that fulfilled as a result of the Government's leadership and actions.
"I would ask Mr Harvie to consider the achievements that have been made so far and to work with the Government on taking forward measures that will have a substantive effect in reinforcing targets in the years to come."