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Police in Melbourne have stressed that the decision to shoot a suspect remains a last resort, after a second police shooting in less than a week.

Officers fired up to eight rounds at a knife-wielding man on Friday morning, only five days after a suspected car thief was gunned down and sent to hospital.

Victoria Police Assistant Commissioner Andrew Crisp says officers only pull the trigger when their own lives are put at risk.

"It's unfortunate this week we've had two incidents occur like that," he told reporters on Friday at the scene of the latest shooting.

"It's not something our members actually want to get involved in.

"It's a difficult decision to draw your firearm and then pull the trigger, knowing you're potentially going to take the life of another person."

Police were called to a house in Elizabeth Street, in the city's western suburb of St Albans, about 10.40am (AEDT) on Friday after reports a woman had been injured.

Police investigate scene after officers open fire on man allegedly armed with knives. Photo: 7News

Three officers spoke to a man at the front door before he came towards them with three knives, police say.

"The police immediately backed off ... calling on this person to put down the knives," Mr Crisp said.

"As they backed away, the male person continued to move towards police and one police officer made a decision to discharge a firearm."

But one officer then tripped, prompting a second officer to continue firing.

The man fled inside the home, where he was later arrested and taken to hospital with multiple injuries, but it's yet to be determined whether they are bullet wounds or self-inflicted knife wounds.

"My understanding is there was not much of a struggle," Mr Crisp said.

A woman inside the house was found with injuries.

Police could not confirm the relationship between the shot man and the woman.

The man remains in the Royal Melbourne Hospital with serious, but not life-threatening injuries.

The woman was taken to the same hospital with serious injuries that are also not life-threatening.

On Monday, police investigating stolen cars shot a man near Melbourne's Etihad Stadium.

Officers were allegedly threatened by the man, who was armed.

That man is still recovering in hospital.