The terracotta relief is thought to have been made by a craftsman from the ancient city of Babylon, about 55 miles (90km) from what is today Baghdad.

It will be sold abroad unless the British Museum can raise the price — believed to be £1.5 million — although the owner, a Japanese collector, is keen for the sculpture to go to the museum.

John Curtis, keeper of the museum’s Department of the Ancient Near East, described it as the second most important Babylonian piece in existence, after the stele in the Louvre on which King Hammurabi’s law code is inscribed.

“It is enormously important. It’s iconic, an incredible piece. There’s absolutely nothing like it,” he said.

Neil MacGregor, the British Museum’s director, and the trustees would like to make the carving the museum’s principal acquisition for its 250th anniversary.

Dominique Collon, curator in the Department of the Ancient Near East, said that the exceptional quality of the piece suggested that, if the figure was a prostitute, she must have come from “a very high-class establishment”.

Other interpretations suggest that the relief may depict Ishtar, the goddess of sexual love and war, or the goddess Ereshkigal, her sister and rival, who ruled the Underworld.

The winged figure wears a horned head-dress, a necklace and bracelets. She is holding a rod and ring, indicating that she could be a goddess. Her legs end in the talons of a bird of prey and rest on the backs of two lions. The figure, flanked by owls, appears to be standing on mountainous terrain. Although lions are associated with Ishtar, she is always shown armed and does not have bird’s talons, which suggest a link with the Underworld. Despite some breaks and cracks, the relief is in extraordinarily good condition.

Its precise history is unknown. It surfaced in the 1920s, in the possession of a Beirut dealer and came to London, where it was acquired by Norman Colville, a noted collector.

The British Museum was first offered the piece in 1935 but could not justify purchasing it when the country was in the throes of the Depression.

The plaque, 49.5cm (20in) high by 37cm wide, was sold to a London dealer, Sidney Burney, and then twice at auction, at Sotheby’s and then at Christie’s, but remained beyond the British Museum’s budget.

Although it is one of the world’s most important Babylonian treasures, it has rarely been seen by the public apart from when it was loaned to the British Museum between 1980 and 1991 by the current owner, who has had it since 1974.

While negotiations and fundraising take place, the relief remains in the British Museum’s storerooms.

Dr Collon said: “Now we have been given a fourth, and no doubt last, opportunity to acquire this remarkable and famous piece, which would be a stunning addition to the collection.” She said that although it was considerably smaller than the Louvre’s stele, it equalled its “quality of execution and surpassed it in iconographical originality”.

The British Museum, which boasts the greatest collection of Mesopotamian antiquities outside Iraq, would give it pride of place among artefacts belonging to the age of King Hammurabi, under whose reign (1792-1750BC) Babylon came to prominence.

The attempt to acquire the relief comes as the museum experiences a huge increase in visitors to its Mesopotamian and Assyrian galleries, with the public developing a yearning to know more about Iraq’s great archaeological heritage. Mesopotamia, the land between the rivers Tigris and Euphrates, was home to Sumerians, Babylonians and Assyrians.

Iraq’s heritage is that of the world, the cradle of civilisation and the site of the fabled cities of Ur, Babylon and Nineveh. Cuneiform writing, glass and accounting were all invented there.

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