South Lanarkshire Council has already approved a planning application to allow Mexican aggregates firm Cemex to expand the Hyndford Quarry at New Lanark into a buffer zone around the nearby World Heritage Site.
The area attracts 350,000 annual visitors and the contentious plans have already prompted more than 11,000 objections.
MSPs and conservation groups are now appealing to Derek Mackay to call in the planning application for the decision to be made by ministers. The planning minister also faces opposition from within his own party.
The SNP's Aileen Campbell, MSP for Clydesdale, claimed around 95% of her constituents opposed the development.
She said: "Many residents were concerned about the impact of the quarry on the long-term historic integrity of the New Lanark setting, and as cultural tourism has great economic importance for the area, we need to be given strong and robust reassurances that this will be protected."
Joan McAlpine, the SNP MSP for South of Scotland, added: "I believe this sends out a very bad message about the Scottish Government's commitment to conservation."
A government directive issued in 2009 gives Scottish ministers the power to intervene in local planning decisions when applications are deemed to be of national importance.