Police have released footage of an officer killing a neo-Nazi gunman, quickly ending a mass shooting that left eight people dead and seven others hurt at a Dallas shopping centre.

The edited five-and-a-half-minute video details the final moments of Mauricio Garcia, 33, after he unleashed a rain of bullets from an AR-15-style rifle at the Allen Premium Outlets on May 6.

Those killed included three members of a Korean American family including a three-year-old child, two young sisters, a security guard and an engineer from India.

Police have not revealed a motive for the attack.

The shooting came in a year that has seen an unprecedented pace of mass killings.

The footage from a body camera worn by an Allen police officer starts with him telling two children outside the mall to wear their seatbelts and be good.

Moments later, the sound of rapid gunfire erupts.

The children and a woman with them run away as the officer radios in the report, grabs his rifle from his car and runs toward the gunfire, the footage shows.

As he runs, the panting officer shouts at people to move and get out.

At one point he tells the dispatcher: “I believe we’ve got a mass shooter,” and shouts at the gunman to drop his weapon.

“I’m passing injured (people),” he adds.

The officer continues to run through the outside galleries of the outlet as the sound of gunfire bursts continues.

About four minutes into the video, the officer opens fire with at least six shots.

An instant later, the officer shouts: “Drop the gun,” and then reports: “I’ve got him down.”

Another officer then confirms the gunman is dead.

The video ends with the two officers standing next to the gunman’s body, which is blurred out.

The footage was released a day after a grand jury cleared the officer of wrongdoing, indicating “the use of force was justified under Texas law,” according to a police statement.

In the statement, Allen Police chief Brian Harvey praised the officer.

“This video shows how quickly a routine interaction with the public turned into a life-and-death situation,” Mr Harvey said.

“The officer recognised the danger, ran toward the gunfire and neutralised the threat — and for his actions, the Allen community is forever grateful.”

Three members of a Korean American family were killed: Kyu Song Cho, 37, Cindy Cho, 35, and their three-year-old son, James Cho. Their six-year-old son was hurt.

Also killed were Aishwarya Thatikonda, 27, sisters Daniela Mendoza, 11, and Sofia Mendoza, eight, security guard Christian LaCour, 20, and Elio Cumana-Rivas, 32.

Garcia used one of eight legally bought guns he had taken to the shopping centre, authorities said.

The killer had no criminal record.

An army official said Garcia failed to complete basic training about 15 years earlier and was kicked out for mental health reasons.

The official spoke on the condition of anonymity to discuss personnel matters.

Garcia left a long trail of online posts describing his white supremacist and misogynistic views.

He described mass shootings as sport and posted photos showing his large Nazi tattoos and a favourite passage in the Hunger Games books marked with a swastika drawn in green highlighter.

He was Latino and posted a cartoon image showing a Latino child at a fork in a road, with one direction labelled “act black” and the other “become a white supremacist”.

“I think I’ll take my chances with the white supremacist,” he wrote.