Members of the group Save Our Landscapes were dismayed last year when South Lanarkshire Council approved a plan by cement company Cemex to extend Hyndford Quarry into a zone surrounding the 18th century preserved mill town near the Falls Of Clyde.
However, Scottish Government Planning Minister Derek Mackay has called in the plans and a Reporter will be appointed to carry out an investigation before any decision is made on whether the quarry can go ahead.
It means the Government will make the final decision.
Professor Mark Stephens, of Save Our Landscapes, said he was delighted with the news and that the group would be ready to make new submissions to the Scottish Government if required.
He said: "This is great news. We made a strong representation to the Government, along with the International Council Of Monuments And Sites, the New Lanark Trust and the Garden History Society.
"We have always thought this is a proposal that should have been called in because of the international importance of the site.
"The issue at stake is the security of Scotland's natural heritage and it is right the Government will have a say."
New Lanark was established in 1785 as a cotton mill village and holds a special place in Scotland's cultural history after becoming the focus of Robert Owen's utopian socialism, which provided residents with free health care and affordable education.
The Falls Of Clyde are surrounded by a nature reserve managed by the Scottish Wildlife Trust. It is home to more than 100 species of birds, including a pair of nesting peregrine falcons.
Cemex's proposal to extend the quarry into the buffer zone has been opposed by some MSPs, with a group of 20 parliamentarians from across the political divide signing a motion for Scotland to protect its history.
James Simpson, vice-president of the International Council For Monuments And Sites, has warned the project risks undermining Scotland's reputation for safeguarding its heritage.
Cemex UK Operations wants to extend its current sand and gravel quarry inside the buffer zone, which is part of the Clyde Valley Woodlands National Nature Reserve, a site of special scientific interest and special area of conservation.
A Government spokesman said: "Scottish ministers will consider a planning application for the proposed extension to Hyndford Quarry.
"The extension lies inside the buffer zone of the site and Falls Of Clyde Inventory Designed Landscape, and is adjacent to New Lanark Conservation Area, part of the Clyde Valley Woodlands National Nature Reserve, a Site Of Special Scientific Interest and special area of conservation.
"A Reporter will be appointed to examine the proposal and make a recommendation to ministers on whether planning consent should be granted."