A man has been shot dead by police after allegedly attacking two constables in central Newcastle, leaving them with serious stab wounds. 

One of the officers was stabbed in the chest while the second suffered injuries to her hands, NSW Police said in a statement on Friday.

The constables were responding to reports of a theft at a home on Bishopsgate Street in Wickham at around 8am on Friday.

On arrival, they were allegedly threatened then stabbed by the knife-wielding man who was then shot dead.

Both constables were taken to John Hunter Hospital in serious but stable conditions.

A critical incident team will investigate the circumstances surrounding the incident, including the discharge of a police firearm.