An armed man has been shot dead by police at the scene of an alleged domestic violence incident in Sydney’s southwest.

A critical incident investigation is underway after the 29-year-old was shot in the chest in William Street at Yagoona shortly before 9am on Sunday.

Police say officers responding to reports of a domestic violence-related incident were threatened by the man, who was reportedly armed with a knife.

A Taser was deployed before a police officer discharged his firearm.

Officers rendered first aid before the man was treated at the scene by ambulance paramedics, but he later died in Liverpool Hospital.

A critical incident team comprised of officers from the Homicide Squad will investigate the circumstances surrounding the incident, including the discharge of the firearm.

That investigation will be subject to independent review.