A man has been shot dead by police during an assault on two women in inner-city Sydney.

It was the second person shot by NSW Police within just a few hours.

The man suffered fatal gunshot injuries at a property on St Neot Ave in Potts Point about 10.50am on Tuesday.

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He had entered the unit complex armed with a weapon and assaulted two women inside, NSW Police said.

The women, aged 48 and 56 who police believe were from different units in the housing complex, are both in hospital with head and facial injuries.

“One (has) more significant injuries than the other but they are not believed to be life-threatening,” NSW Police Assistant Commissioner Peter McKenna said.

Both women are reported to be in stable condition.

Police said the man was seen with a knife.

McKenna said while the exact cause of the women’s injuries is still under investigation, the injuries of at least one of them is “consistent with being assaulted by a weapon”.

The other injuries appear to be the result of blunt force trauma, he said.

The two women are not believed to have been known to the man.

He also threatened responding police, who tried unsuccessfully to taser him before one gunshot was fired at him.

He died a short time later in the care of responding NSW Ambulance paramedics.

“The police officers are pretty traumatised at the moment,” McKenna said.

“To take a life, that’s the last thing we want to do.”

The critical incident investigation will be subject of an independent review by the Professional Standards Command and overseen by the Law Enforcement Conduct Commission.

NSW Police shot another man earlier on Tuesday during an unrelated incident in Newcastle.

A 36-year-old man was hospitalised with a gunshot wound to the shoulder, after he allegedly threated police with an edged weapon.

Police had forced entry into the Honeysuckle Dr unit during an arrest attempt about 8.30am.

He remains in hospital under police guard.