Jacob Blake, 29, was shot and injured by police as he leaned into his car on Sunday, with his children screaming.
Two people have been killed and one injured during a third night of unrest in the US city of Kenosha, sparked by the police shooting of a black man.
Tuesday night’s incident was believed to have involved protesters against Mr Blake’s shooting and armed men guarding a petrol station.
The protests have at times have turned violent, causing damage to property.
Mr Blake is in hospital, and his mother said he was conscious. Mr Blake’s lawyers say it will take “a miracle” for him to walk again.
In their statement, Kenosha Police said officials responded to “reports of shots being fired and multiple gunshot victims” in the city at about 23:45 on Tuesday (04:45 Wednesday GMT).
“The shooting resulted in two fatalities and a third gunshot victim was transported to a hospital with serious, but non-life threatening injuries,” the statement said.
It added that the identities of the victims were still being determined and that no further details would be given at this time. An investigation has been opened.
Kenosha County Sheriff David Beth earlier told the New York Times that an investigation into the shootings would be focused on a group of men armed with guns outside a petrol station.
Footage shared online showed a man with a rifle being chased by a crowd before he fell to the ground and appeared to fire multiple rounds at them. Other video shows armed civilians, many dressed in military fatigues, congregating outside businesses they said they were protecting.
Previous protests have resulted in damage to government offices and private businesses, and there have been reports of vigilantes turning out to protect property.
A spokesman for the Wisconsin Professional Police Association told the BBC individuals and groups were exercising their own form of vigilantism because law enforcement was spread very thin across the city.
Wisconsin Governor Tony Evers said on Tuesday he was sending more National Guard troops to the city amid the unrest.
Media reports quoted White House Chief of Staff Mark Meadows as saying Mr Evers had turned down an offer of federal support.
Officials in Mr Evers’ administration said the offer was for help from the Department of Homeland Security and had been turned down because more National Guard members were already on their way.
How have the protests unfolded?
Within hours of Mr Blake’s shooting on Sunday, hundreds of people had marched on Kenosha’s police headquarters. Cars were later set alight, and police urged 24-hour businesses to consider closing because of “numerous” calls about armed robberies and shots being fired. A night-time curfew was imposed.
On Monday, Governor Evers called up the National Guard to help local police. The forces used tear gas, rubber bullets and smoke bombs, protesters said. Some demonstrators were seen attacking cars and property with baseball bats, Reuters reported.
On Tuesday, hundreds of protesters marched through the city. A small group threw fireworks and water bottles at police, who responded with rubber bullets and tear gas.
In a message posted on Twitter, police urged people in Kenosha, a city of about 100,000 on the south-western shore of Lake Michigan, to “stay off the streets”.
Buildings and cars have been burned.
A state of emergency has also been declared in Wisconsin.
Protests have also spread to a number of other cities, including Portland, Oregon and in Minneapolis, Minnesota, where the police killing of unarmed black man George Floyd in May sparked Black Lives Matter protests across the US and globally.
The Toronto Raptors basketball team, who won last year’s NBA championship, have discussed potentially boycotting an upcoming conference semifinal game in response to Mr Blake’s shooting.
Player Norman Powell said the situation had gotten to a point where just saying “Black Lives Matter” was not enough.
“I think everybody’s at the point of sitting up here and saying ‘Black Lives Matter’ and sitting up having discussions and Zoom calls… That’s not getting the job done. Taking a knee for the anthem, that’s not getting the job done.”
What’s the latest with Jacob Blake?
Lawyer Ben Crump told a press conference on Tuesday that doctors said Mr Blake had been paralysed by the shooting.
“His family believe in miracles, but the medical diagnosis right now is that he is paralysed and, because those bullets severed his spinal cord and shattered some of his vertebrae, it is going to take a miracle for Jacob Blake Jr to ever walk again,” he said.
The 29-year-old, shot as his young sons sat in the car, was also left with holes in his stomach, an arm injury and damage to his kidney and liver. Most of his colon and small intestine had to be removed, his lawyers told reporters.
His mother Julia Jackson told the press conference her son had been “fighting for his life”, but said if he “knew what was going on as far as that goes, the violence and the destruction, he would be very unpleased”.
Mr Blake’s shooting comes as the US grapples with the treatment of African-Americans at the hands of law enforcement, as well as wider questions about racism in society, since the death of George Floyd.
In her speech, Ms Jackson addressed racism directly and called for “healing”.
“Do you understand what is going to happen when we fall – because a house that is against each other cannot stand.”
What do we know about the shooting?
Police say they were responding to a domestic incident when they went to the site of Sunday’s shooting but have given few other details. So far it is unclear who called the police, how many officers were involved, and what happened before the shooting.
Footage of the incident shows Mr Blake opening the door and leaning into the car, at which point one officer grabs his shirt and opens fire. Seven shots can be heard in the video, as witnesses shout and scream.
Mr Blake’s fiancée Laquisha Booker, said the children – who witnessed everything as they sat in the back of the car – were screaming as their father was shot.
Lawyers for Mr Blake said he had been trying to “de-escalate a domestic incident”. Witnesses said the same to local media.
Court records show there was an open arrest warrant against Mr Blake on sexual assault and domestic abuse charges but police have not said if officers were aware of this when they responded to the call on Sunday.
Wisconsin’s Department of Justice is investigating the incident in Kenosha, while the officers involved have been placed on administrative leave. A petition calling for them to be charged has garnered tens of thousands of signatures.
Mr Blake’s father has said he does not have confidence in the investigation.
“Anybody that is white, that is doing an investigation about a black young man that was shot seven times in his back, and haven’t come up with an answer or a comment at this point, is not welcome,” he told reporters.