British scientists are to begin work on a revolutionary project to record three-dimensional models of world heritage sites so that they can be re-created if they fall victim to climate change, natural disaster, war or terrorism.

The team of six – from Historic Scotland and the Glasgow School of Art – will team up next month with an American company, CyArk, to shoot laser beams at Mount Rushmore in South Dakota, creating a 3D model accurate to within 3mm, digitally preserving the carved faces of former presidents George Washington, Thomas Jefferson, Theodore Roosevelt and Abraham Lincoln should archaeologists need to repair them.

Funding for the project was rushed through because of concerns over the deterioration of the granite rockface.

CyArk has identified several other "at-risk" sites, including the Acropolis in Athens, threatened by acid rain, and Machu Picchu in Peru, which suffers from excessive tourism. Pollution, over-expansion and deforestation may have already permanently damaged Tikal National Park in Guatemala, one of the largest archaeological remains of the pre-Columbian Maya civilisation.

CyArk's ultimate aim is to create 3D models of 500 sites around the world. Work began this year on scanning the underworld of Rome, 170km of winding catacombs dating back two millennia, and the Zapotec capital of Monte Albán, in Mexico. Other sites proposed for digital mapping include Angkor Wat in Cambodia, the Khmer temple complex built for King Suryavarman II in the early 12th century, Thebes in Egypt and Pompeii, the Roman town buried by the eruption of Mount Vesuvius.

Digital scanning might have saved some of the historic buildings destroyed in the L'Aquila earthquake in Italy in April. They include Santa Maria di Collemaggio, the church that was the site of the coronation of Pope Celestine V in 1294, and Porta Napoli, Naples's oldest gate, built in 1548 in honour of the Holy Roman Emperor Charles V. David Mitchell, director of the technical conservation group at Historic Scotland, cites the Buddhas of Bamiyan in Afghanistan – blown up by the Taliban in 2001 – as another example of what could have been saved by the new technology.

Although the Japanese government has pledged to help rebuild the giant monuments, carved from sandstone cliffs, it will be difficult to replicate the originals. "If only they had been scanned, we could have helped rebuild them to their original state," said Mitchell.

CyArk, founded by Ben Kacyra, the "John Logie Baird" of laser technology, teamed up with Historic Scotland and Glasgow School of Art after witnessing the latter's pioneering work at digital documentation conferences in the United States and Scotland.

Mitchell said the Americans were amazed by the Scottish team's technical capabilities, which have been used to create 3D models of Stirling Castle and Rosslyn Chapel in Midlothian. "When Ben saw the work we were doing he said we were miles ahead of anyone else and was blown away," said Mitchell. "We have worked with Glasgow School of Art for a number of years on laser scanning and became the first group to use this technology on heritage sites. It can pick out millions of points on a monument down to an accuracy of 3mm, which has never been done before. It's cutting-edge stuff. Working on Mount Rushmore will give us the opportunity to put Scotland on the world stage."

Michael Russell, Scotland's minister of culture, said the link with CyArk was the beginning of what he hoped would become "a successful long-term international partnership".

Speaking from the US, Kacyra told the Observer he was delighted the Scottish team was on board for the five-year project. "I was amazed at their advanced work," he said. "I had never seen any government organisation acquiring this kind of scanner and then start experimenting with it in the heritage field. We are indebted to Historic Scotland for their very generous donation of resources and technology."

Scanning is almost complete on New Lanark's world heritage site, a restored 18th century cotton mill in southern Scotland. Once work is complete at Mount Rushmore in October, the team will move to Skara Brae, "the heart of Neolithic Orkney", which is under threat from coastal erosion. The Antonine Wall, St Kilda and the Old and New Towns of Edinburgh are the remaining Scottish world heritage sites to be scanned.

The remaining four international sites have yet to be decided, but the Taj Mahal in India and the Longmen Grottoes in China, 2,345 niches carved from rock that house more than 100,000 statues, have been suggested as possibilities.

Several European companies have already expressed "huge interest" and have said that they are eager to utilise Historic Scotland's scanning equipment for the preservation of other world heritage sites.

Kacyra added: "I hope we can continue our collaboration beyond the Scotland 10 and CyArk 500 and eventually transfer our technology to developing countries."