During his meeting with Modi, Abbott returned the idols, one of which is a Nataraja --the dancing Shiva-- which belonged to the Chola dynasty of 11th-12th century.
The other sculpture is of Ardhanariswara, which represents Shiva in half-female form, and dates back to 10th century.
Both the statues were allegedly stolen from temples in Tamil Nadu and their return was sought by India in March.
The Nataraja statue, cast in bronze, was purchased by the National Gallery of Australia (NGA) in February 2008 at a price of USD 5.1 million from art and antiquities dealer Subhash Kapoor who was then based in New York.
The Ardhanariswara statue was purchased by the Art Gallery of New South Wales in 2004 for approximately 300,000 Australian dollar (USD 280,979).
In 2012, Kapoor, owner of the "Art of the Past" gallery in New York, was arrested in Germany and subsequently extradited to India. He is accused of conspiracy to commit burglary and smuggling from Tamil Nadu antique idols of Hindu deities belonging to Chola dynasty.
In March, the Ministy of External Affairs had through India's High Commission in Canberra made a formal proposal to the Australian Department of Attorney General by forwarding the request of the Tamil Nadu police for the return of the two idols.
