Civil liberties groups have called for an independent inquiry into the shooting of two Aboriginal teenagers in Sydney's busy Kings Cross nightlife area at the weekend.

Police shot the teenagers, aged 14 and 18, when the stolen vehicle they were driving mounted a crowded pavement in the early hours of Saturday morning, hitting two women. Four other males, aged 13, 14, 16 and 24, were in the back seat and not hurt.

Graphic mobile phone footage showed the violent arrest of one of the teenagers. He was dragged out of the car, handcuffed and held face down on the pavement, while bleeding heavily.

The incident sparked protests at a rally outside the New South Wales state parliament on Tuesday. At the rally, Aboriginal activist Graham Merrit accused the police of racism over the shooting.

"It's time to stand up all you young fellas and be counted. Don't let this happen to you any more," he told the ABC.

Another well-known Aboriginal figure, Anthony Mundine, also at the rally, condemned the shooting.

"I feel that it's brutality at its best. Who shoots teenage kids, unarmed, cornered, trapped, ready to be arrested?" he said.

Police have launched an internal investigation into the shooting, which will look at whether officers were right to open fire on the car. The New South Wales police minister, Mike Gallacher, defended the action.

"Cops had seconds to make a decision. If someone's not going to stop the car … and you've got a young woman on the front of the vehicle, you know, until such times as shown otherwise, I'm going to back the cops," he said.

Gallacher said he was confident the matter would be properly investigated.

But David Bernie, the vice-president of the New South Wales Council for Civil Liberties, said an independent inquiry must take place.

"Otherwise this is really just the police investigating the police and we don't think that's satisfactory when there's a real issue of public safety involved," he said. "My main concern is the discharge of firearms in such a public place."

Bernie said the incident called into question police training and why officers did not shoot at the wheels of the car instead of its occupants. He also said the shooting risked inflaming already tense relations between police and the city's Aboriginal community.

Both teenagers shot in the incident remain in hospital.

The incident followed the death of a 21-year-old Brazilian last month after police shot him with a stun gun.