The man entered the building and began assaulting the women in two units in the well-heeled suburb of Potts Point in Sydney about 10.50am on Tuesday, police said.
Arriving police deployed a taser to control him but it was ineffective.
The alleged attacker then confronted police before an officer fired a single shot, hitting the man.
He died at the scene, Assistant Commissioner Peter McKenna said.
The man was not immediately identified and the precise location of the shooting in St Neot Avenue has not been revealed.
The women, aged 48 and 56, suffered facial injuries and were taken to hospital.
Mr McKenna would not speculate on why the stun gun was ineffective.
"Tasers have been an effective part of our arsenal," he told reporters on Tuesday.
"They are a less-lethal option but like anything they're not always successful.
"(Police) don't come to work to be confronted by this type of thing or take a life - that's the last thing we want to do."
He underscored that officers had been responding to the women in distress when the situation escalated quickly.
A crime scene has been set up, with officers using sheets to cover the dead man, who is believed to be aged in his late 30s to early 40s.
The street was cordoned off with a helicopter flying above the scene and up to 20 riot cars, police vehicles and ambulances descending on the block.
The investigation will be reviewed by the Professional Standards Command and overseen by the Law Enforcement Conduct Commission.
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