Armed man shot dead by police after allegedly attacking two women in inner-city Sydney

An armed man has been fatally shot by police after he allegedly broke into a unit block and attacked two women in what police believe was a random attack in the Sydney suburb of Potts Point this morning.

Police were called to a unit complex on St Neot Avenue about 10.50am following reports that a man armed with a knife had broken into the building.

Officers say when the man was confronted, he lunged at them with a knife, and a Taser was fired at him.

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Police said the Taser was "ineffective", and a single round was fired at the man. He was later pronounced dead.

Neighbour Alex Dobelle told 9News he witnessed the entire ordeal.

"I was sitting by the pool and could hear a woman screaming for help.

"We could hear a lot of police cars coming down."

It is believed the man barricaded himself inside one of the apartments during the 10-minute standoff with police.

The incident came to an end after the man attempted to jump out of the window of one of the units.

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"The way that the lady was screaming for help, it sounded like he may have just come into the house, and he surprised this woman," Dobelle said.

"Then [the police] said, 'Get the f--- back in the house'.

"Then I heard Taser shots, and then they've dragged him away and then next minute I hear some gunshots."

Assistant Commissioner Peter McKenna said police believe the women, aged 48 and 56, were from two different apartments.

Police do not believe either woman knew the man.

"Both those females have head and facial injuries," he said.

"Both have been taken to hospital, one with more significant injuries than the other, but both are believed not to be life-threatening."

One of the women had injuries suspected to be from a stabbing, while the other suffered blunt force trauma.

Both suffered wounds to their heads and faces and have been taken to St Vincent's Hospital in a stable condition.

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McKenna said the responding officers were "pretty traumatised" following the incident.

"They don't come to work to be confronted by this type of thing or to take a life.

"That's the last thing we want to do.

"We will thoroughly investigate this and get to the bottom of why and how [the shooting] occurred."

A critical incident has been declared.

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