The Indian government formally requested the return of a 900-year-old Dancing Shiva statue from the National Gallery of Australia and a stone sculpture of the god Ardhanarishvara from the Art Gallery of NSW last week.

The Attorney-General's Department issued a statement on Wednesday saying that the Art Gallery of NSW had "voluntarily removed" its sculpture from public display – one day after it was announced the National Gallery would remove its allegedly looted statue from exhibition.

Both artefacts were bought from antiquities dealer Subhash Kapoor, who is on trial in India for looting and wanted in the United States for allegedly masterminding a large-scale antiquities smuggling operation.

A first secretary of India's High Commission, Tarun Kumar, said it was "our expectation" both statues would be returned to India. "We expect a decision in that regard will be taken within the next month," he said.

A spokeswoman for the Attorney-General's Department said on Wednesday that there was no time limit in the legislation for responding to the Indian government's request.

The Canberra-based National Gallery paid $US5 million for the Dancing Shiva statue in February 2008. The statue was one of 22 items it bought from Mr Kapoor's Art of the Past gallery for a total of $11 million between 2002 and 2011.

The Art Gallery of NSW bought six items from Mr Kapoor, including the Ardhanarishvara sculpture for $300,000 in 2004, as well as others that lack an ownership history.

A spokeswoman said the gallery would co-operate fully with the government to resolve issues concerning the provenance of its collection.

The Indian government is not obliged to compensate the two galleries for the return of the two statues.

Mr Kumar said further requests for the return of antiquities would depend on the investigating agency, the Tamil Nadu police.

Duncan Chappell, a Sydney University criminologist who specialises in art crime, suggested the galleries should voluntarily return any objects in their collections that are found to be stolen.

"I think the more rapidly this occurs the better," he said. "They shouldn't have to wait for formal requests to be made if there is evidence these are objects of very dubious if not false provenance."