In a joint statement, the 30 leaders said the levy is a “tax on jobs” and could cost commuters as much as £500 each.
MSPs will vote on the Scottish Government Budget on Thursday, which is expected to pass after a deal was agreed with the Scottish Greens.
Part of that agreement was the introduction of the parking tax.
Tory finance spokesman Murdo Fraser said: “Right across Scotland, Scottish Conservatives are making it clear that we oppose this unwanted, poorly thought out tax.
“From Holyrood to local councils across Scotland, we will fight to stop it being introduced.
“Nicola Sturgeon has tried to argue that this won’t impact people if their local council doesn’t adopt it - tell that to the tens of thousands of people from all over Scotland who commute into our cities and face having to pay up.
“It’s now beholden on SNP councillors to follow suit, follow the lead of the Scottish Conservatives and make clear that they too will oppose these ridiculous plans. That is the least they should do for their constituents.”
Scottish Greens co-convener Patrick Harvie suggested the Tories are being hypocritical over the proposals for the local tax measure.
Mr Harvie said: “They once claimed to support localisation, but the Conservatives are apparently now imposing a national ban on their councillors even considering this new power.
“It’s dismal, but no surprise, that in a month when young people in Scotland and across the world have left their classrooms to demand urgent action on pollution and the climate crisis, the Tories and others are going frantic about car parking while offering nothing positive for people who walk, cycle or use public transport.
“But the increasingly deranged hard right Tories can be expected to ideologically oppose every tax.”