A planned workplace parking levy may not be applied to certain public sector workers, including teachers, the Scottish government has said.

A spokesman for first minister Nicola Sturgeon said the issue of whether groups such as teachers should pay the new charge could be considered when the matter came before the Scottish Parliament’s Rural Economy and Connectivity Committee.

The Conservatives demanded had a “full consultation” be carried out on workplace parking charges and accused ministers of trying to “sneak” plans for a levy through the Scottish Parliament.

The Scottish government has already committed in principle to support changes to legislation already going through Holyrood that would give councils the power to introduce a charge on workplace car parking.

The proposal was part of a deal struck between the Scottish Greens and finance secretary Derek Mackay to pass the budget through parliament, although SNP ministers insisted any new levy would not be applied to hospitals and other NHS buildings.

Opposition MSPs have demanded to know why other public sector workers, such as teachers, might have to pay the charge.

Ms Sturgeon’s spokesman said the exemption “could quite possibly” be extended because details on the proposals for a workplace car parking levy had not yet been agreed.

The Tories said the government had previously pledged to hold a consultation before any such charge was introduced.

Conservative finance spokesman Murdo Fraser said: “Yet, now they want to sneak it through, all in order to buy off their friends in the Greens.

“The car park tax is a complete mess. The SNP must, for once, listen to people and think again.”

The Scottish government has agreed in principle to support Green amendments to the Transport (Scotland) Bill, which would give councils the power to bring in a workplace parking levy.

Ms Sturgeon’s spokesman said: “This was a Green proposal brought forward as a condition of their support for the budget. It’s not a Scottish government proposal.”