Sydney, Jul 17 (IANS): Police in the Australian state of New South Wales (NSW) confirmed on Monday that a critical incident investigation was underway after a man was shot dead during an operation.

"It is reported that he had sustained a gunshot wound, which is suspected to be self-inflicted," NSW Police Force said in a statement, adding that the identity of the 29-year-old man remains to be formally confirmed.

According to the statement, at about 12.15 p.m. on Sunday, police officers were called to a home at Bowenfels -- a town on the western outskirts of Lithgow, responding to reports about a man and woman fighting at the property, reports Xinhua news agency.

The man was believed to possess a firearm.

On arrival, officers spoke briefly with the pair from a distance before they went inside, locked the doors, and refused to come out.

NSW Police Force said that at about 4.20 p.m., a number of shots were fired from the home in the direction of police, with police returning fire.

"No one was injured during the exchange," the police noted.

On Monday morning, the 20-year-old woman came out of the property, and then police officers gained entry to the home.

The man was found dead with gunshot wound, according to reports, which was suspected to be self-inflicted.

The police said that an investigation has commenced into all circumstances relating to the incident and the woman is continuing to assist police with inquiries.