The bloodshed happened just before midnight in the hours after an 8pm curfew that was intended to quell days of unrest over the death of George Floyd in Minnesota.

All three injured officers were expected to recover. The man who attacked them was shot multiple times and was hospitalised in critical condition, said Police Commissioner Dermot Shea.

"What we know at this point and time is that it appears to be a completely, cowardly, despicable, unprovoked attack on a defenceless police officer and thank God we aren't planning a funeral right now," Shea said.

He noted that it was one of several attacks on police officers in recent days, including one in which a driver ploughed into a police sergeant who was trying to stop looting in the Bronx and a lieutenant who was struck in the helmet by a brick during a brawl with protesters in Manhattan.

New York City has been roiled by days of protests over police brutality, and the spot in Brooklyn where Wednesday night's attack took place is just a block away from where demonstrators and police engaged days ago in an hours-long standoff, during which a police car was burned and protesters beaten with batons.

There were peaceful marches and protests throughout the day on Wednesday, but police moved in to break them up when the city's curfew took effect.

Mayor Bill de Blasio, who appeared with Shea outside the hospital where the officers were being treated, called it a "very tough night" and lauded the officers for their bravery.

Some details of how the attack unfolded were still unclear, but Shea said the man casually approached two officers stationed in the area to prevent looting at around 11.45am and stabbed one of them.

Officers a short distance away heard gunshots, rushed to the scene and saw the man with a gun in his hand, believed to have been taken from one of the officers, Shea said. The responding officers then opened fire.

The commissioner said 22 shell casings were recovered. He didn't say whether the officers' hand wounds came from the guns of fellow officers.

Shea didn't speculate on the motive of the stabber, who was not identified, but Patrolmen's Benevolent Association President Patrick Lynch blamed anti-police rhetoric during the protests.

"Are we surprised? Are we surprised we're here in the hospital again. Did we doubt because of the rhetoric we're hearing, the anti-police rhetoric that's storming our streets, are we surprised that we got this call? I'm not. We said it's going to happen," he said.

Australian Associated Press