A Texas gunman has been arrested after a rampage across the US state left six people dead and three injured, including two police officers, authorities said  Wednesday.

The shooting spree occurred over the span of several hours Tuesday in Austin, where four people were shot dead and the suspect engaged in a shootout with police, and in the San Antonio area where a man and woman were found dead in a home.

"We strongly believe one suspect is responsible for all of the incidents," Robin Henderson, interim chief for the Austin Police Department, said of the Austin killings.

The 34-year-old suspect, who was not identified, "is in custody and no longer poses a threat to our Austin community." 

At least four incidents were tied to the suspect, including two double homicides, the wounding of a police officer near a school, and the non-fatal shooting of a cyclist.

One of the double homicides occurred in San Antonio, 75 miles southwest of Austin.

Police there said they received an alert from Austin authorities to search a house linked to the gunman, where they found the bodies of a 55-year-old woman and a 56-year-old man.

"We don't have a definitive identification at this time. But we are fairly certain who these people are… They are believed to be the parents of the suspect who is currently in custody," said Sheriff Javier Salazar of Bexar County, which includes San Antonio.

"Certainly it's a pretty grisly crime scene," Salazar told reporters. 

He said it is believed the man first committed the Bexar County killings "and then the suspect drove to Austin and did what he did there."

In Austin, police exchanged gunfire with the suspect at the site of a burglary where two victims were found dead. One officer there was injured. The gunman fled in a vehicle and crashed after a car chase with police.

The man was arrested in possession of a firearm and charged with capital murder, Henderson said, describing the incidents as a series of "tragic events and horrific criminal acts."

Salazar said the suspect had been arrested in January 2022 for domestic violence against his parents and a sister. He was freed two months later and ordered to wear an ankle bracelet, which he later cut off, he added.

Shootings are alarmingly common in the United States, a country where there are more guns than people and where attempts to clamp down on the spread of firearms are always met with stiff political resistance.

At the end of October, a man carrying a semiautomatic rifle opened fire in a bowling alley in Lewiston, Maine, then continued his rampage at a bar-restaurant. He killed 18 people and was subsequently found dead from a self-inflicted gunshot.