US police have identified the victims in a shooting that killed three people, including a child, in a Target parking lot.

The victims include Hector Leopoldo Martinez Machuca as well as Adam Chow and Chow’s granddaughter.

“Adam Chow and his 4-year-old granddaughter were pronounced deceased on scene,” a Tuesday statement says. Martinez Machuca was pronounced dead after being transported to a hospital. Chow’s wife sustained minor injuries, the release said.

Authorities said the suspected gunman, Ethan Nieneker, “randomly attacked” Martinez Machuca — a Target employee — in the parking lot on Monday local time.

Nieneker allegedly shot him as he was collecting shopping carts, the release said.

The shooting is one in a spate of deadly gun violence in the US, and follows killings in recent weeks at places normally considered safe – a Montana bar, the offices of the US Centres for Disease Control and Prevention in Atlanta and an office building in New York City.

Austin Police Chief Lisa Davis said Tuesday the victims were picked at random and Nieneker had “serious issues”.

“There were some serious failures here … when you look at potentially some mental illness there,” Davis said.

The firearm used in Monday’s fatal shooting was “acquired through family,” Austin police Sergeant Nathan Sexton said Tuesday.

He also has prior criminal offences, including assault causing bodily injury to a family member, driving while intoxicated and possession of marijuana, Davis said on Tuesday.

It is unclear if Nieneker has made a court appearance or obtained an attorney.

A motive has not been determined and it’s not clear what led to Monday’s gunfire.

The shooting erupted during a busy time of year for retailers, with back-to-school shopping underway.

Police were called at 2.15pm and arrived at the Target parking lot where they found three people shot, Davis said.

After shooting Martinez Machuca, Nieneker ran to a black Jeep Cherokee.

He began firing as the Jeep attempted to evade the gunfire, Tuesday’s police statement said.

He then ran up to Chow’s car, where he shot him and then fired into the backseat, striking the granddaughter, police said.

Nieneker was eventually captured about 32km away in South Austin after someone called police, Davis said.

He was taken into custody after being tased.

Austin Mayor Kirk Watson called the shooting “a sickening, cowardly act of gun violence”.

Target said in a statement it is “devastated by the violence” at the Austin store and is working with law enforcement on the investigation.

“We got really, really lucky,” Lee said.

“And some people didn’t.”

At a Jiffy Lube shop that shares its parking lot with the Target, employees locked the doors as soon as they became aware of the shooting.

Paul Smith, an employee at the oil-change store, saw people running from their cars in the parking lot in a panic, he told the AP.

“I had just gotten back from the Target like a minute before,” Smith said.