The FBI and U.S. Marshals assisted local law enforcement in the search for Broderick, who fled before police arrived.
"We are concerned that he might possibly take a hostage and be himself sheltering somewhere waiting for us to leave", Chacon said.
Travis County District Attorney Jose Garza said in a statement that Broderick had been arrested for sexual assault of a child last June and was released on $50,000 bond.
Interim Austin Police Chief Joseph Chacon said Stephen Broderick was suspected in Sunday's deaths of two women and a man. Chacon said Broderick knew the victims, but didn't elaborate on how or provide a motive for the shootings.
Hospitals turning away COVID patients despite bed availability will face action: Kejriwal
A private hospital in the city closely missed a tragedy Saturday night due to shortage of oxygen, he said. The Delhi Chief Minister is expected to impose a seven-day curfew in the city-state till next Monday.
During a briefing Sunday afternoon, officials announced that 41-year-old Stephen Nicholas Broderick was identified as the suspected shooter.
Editor's note: This article has been updated with more details, including on the suspect and police's revised warning to residents. A preliminary investigation indicated that the suspect knew the victims. Chacon also said a child was involved but that the child has been located and is safe.
Authorities called on people in the area to shelter in place. Police shut down a road, with patrol cars and police tape blocking it off. There are also several ambulances and two SWAT trucks at the scene, and two police helicopters and a drone overhead.
The scene is still active and people are being asked to avoid the area, according to the tweet.
The pace and scale of the shootings have been devastating. Less than a week after the Georgia shootings, 10 were killed at a supermarket in Boulder, Colo. And in the two weeks after, six died in an apparent familicide in Texas and seven in a SC attack, including the gunmen.