The British Museum is facing legal action from a leading heritage preservation organisation over its refusal to allow 3D scanning of a piece in its Parthenon marbles collection.

The Institute for Digital Archaeology said it would serve an injunction against the museum, raising the stakes in the dispute.

The IDA will be filing a complaint with the court by the end of the week in order to get the British Museum to grant their request. Their refusal has been arbitrary.

The institute had hoped to reproduce one of the high relief metopes from the south facade of the temple as proof of concept.

The advocates believe that 3D scanning could be used to create replicas of the classical treasures and help resolve the longstanding row between Athens and London over the patrimony of the Parthenon marbles. The IDA, a supporter of the marbles, said that scans would allow a robot sculptor to reproduce the artworks with sub-millimetre accuracy using the same Pentelic marble from which the originals were chiselled.

The aim of the institute is to give people a chance to see how extraordinary a copy can be.

In the past, low-quality plaster casts have been used to make copies of the sculptures. This will be orders of magnitude greater. It will help people see and feel the potential of this technology.

The acting keeper of Greek and Roman antiquities conceded that digital scanning of the 5th-century BC sculptures couldunlock new discoveries, but the IDA was told by email that its request could not be fulfilled.

The Acropolis in Athens

The Acropolis in Athens. Photograph: Costas Baltas/Reuters

Despite the ban, the team visited the British Museum last week and used an iPad to look at the piece from the floor of the Duveen gallery. The British Museum's own guidelines allow the use of 3D software to capture images of the antiquities in the gallery, and the organisation argued that it was within its rights to do so.

The British Museum was concerned to hear that unauthorized scanning took place in our galleries. It is not possible to routinely accommodate all of the requests that we receive, and any such activity would be a violation of our visitor regulations.

The guidelines clearly authorize exactly what we did, according to the email seen by the Guardian.

Your security staff were eager to learn more about the process and were most helpful and encouraging. I'm pretty sure it was captured by your camera. I hope you will correct your obvious misstatements, as your characterisation of our activities represents a gross distortion of the truth.

After the IDA threatened to take legal action, a museum spokesman told the Guardian that it was not possible to accommodate all requests. It said that it already used cutting-edge technologies to explore and share its collection, and that it had hosted visits from the Acropolis Museum for 3D scanning.

The scanning furore has dismayed officials in Greece at the time of a shift in attitudes among some of the world's leading museums.

Elena Korka is the director general of antiquities and cultural heritage at the culture ministry in Greece. It seems absurd and in contradiction to the museum's role.

The British Museum has held the antiquities since 1816, when they were removed from the Parthenon at the request of the British ambassador to the Ottoman empire.

The antiquities were hacked from the temple at a time when it was a subject nation without a voice or sovereignty. The British Museum says they were acquired legally.

The Greek prime minister, Kyriakos Mitsotakis, has renewed the campaign to get the artworks back with the rest of the monumental frieze in view of the site where the sculptures once stood.

The issue of Greece was placed at the center of talks with the UK prime minister of his love for Greece. As a classics student at Oxford, Johnson supported sending the statuary back to Athens.

There are parts of the metope that could be better scanned with a ladder if a permit was eventually granted.

The director of the IDA believes that the sculptures in the Duveen gallery are not in line with the true aesthetic of antiquity.

He said that reconstructions could help the British Museum.