Texas authorities have named a heavily armed gunman who killed eight people including children at a Dallas shopping mall as Mauricio Garcia, aged 33. The man, from Dallas himself, was shot dead by a police officer who was attending a different call in the area.

The gunman in Saturday’s attack used an AR-15 style rifle and wore combat gear, President Joe Biden said.

Investigators quoted by US media say he may have had far-right links, as suggested by a clothing patch he wore.

Two sources told CBS News that the patch bore the letters RWDS, standing for “Right Wing Death Squad” – believed to be a neo-Nazi group.

Police searched a nearby hotel where Garcia was staying, as well as a home in the city, reports say. He opened fire on shoppers at the Allen Premium Outlets mall, in the north Dallas suburbs.

Garcia also had a handgun, and more weapons and ammunition were found in his car, an investigator said.

At least three injured victims remained in critical condition on Sunday.

A law-enforcement source told CBS that he used an assault weapon to gun down his victims and multiple rounds of ammunition were found on his person. He was wearing armoured ballistic gear.

Investigators are combing through social media and online accounts looking for clues as to whether he may have had links to domestic violent extremists and like-minded individuals.

President Biden called for a ban on such assault rifles earlier on Sunday, lamenting what he called “the latest act of gun violence to devastate our nation”.

Confirming that children had been killed in the attack, the president said that “too many families have empty chairs at their dinner tables” – and called once again on his political opponents in the Republican party to support tougher gun controls.

Garcia was reportedly working as a security guard at the time of the shooting and did not have a serious criminal record.

President Biden has ordered the US flag to be flown at half-mast on federal buildings. His call for tighter gun controls, however, was seen differently by Texas’ Republican governor Gregg Abbott.

Speaking to Fox News Sunday, he said his aim was to target the possession of weapons by criminals and deal with a rising mental health crisis, rather than consider wider bans.

“This is something that we have been grappling with over the past year, and there are some potential easy solutions such as passing laws, that we’re working on right now, to get guns out of the hands of dangerous criminals and to increase penalties for criminals to possess guns,” he said.

“One thing that we can observe very easily and that is there has been a dramatic increase in the amount of anger and violence that’s taking place in America. And what Texas is doing in a big-time way, we are working to address that anger and violence by going to its root cause, which is addressing the mental health problems behind it.”