A billionaire family in the United States will return more than 30 looted ancient artefacts to Cambodia after agreeing it "wrongfully possessed" the treasures, the Cambodian government said Wednesday.

Years of civil war followed by the genocidal Khmer Rouge rule saw historical sites looted with near-impunity in Cambodia, which is famed for its Angkor Wat temple complex.

Many of the pieces are thought to date back to the Khmer Empire, a once-mighty dynasty that sprawled across much of modern-day Cambodia, Thailand, Vietnam and Laos between the ninth and 15th centuries.

A trove of stolen artefacts has been sent back to Cambodia in recent years from Western museums and private collectors.

Now, 33 items from the Lindemann private collection will be "voluntarily" returned to Cambodia, its ministry of arts and culture said Wednesday.

The move "sets an excellent and proper example for other museums and private collectors… to follow and return our national treasures," Minister of Culture and Fine Arts Phoeurng Sackona said.

The government did not say when the items will arrive in Cambodia.

They include a reclining Vishnu and Ardhanarishvara sculpture — believed to be from the remote northern ancient city of Koh Ker — which witnesses say was looted in the 1990s, according to the official statement.

"Having purchased these items from dealers that we assumed were reputable, we were saddened to learn how they made their way to the market in the United States," The New York Times quoted the Lindemann family as saying in a statement.

Last month, the National Gallery of Australia said it will return three sculptures to Cambodia after an investigation found they were likely to have been "illegally exported".

The bronze sculptures from the 9th-10th century were bought for $1.5 million in 2011 by British art dealer Douglas Latchford, who was later "convincingly implicated in the illegal trade of antiquities", the gallery said.