By Alex Dobuzinskis

(Reuters) - A gunman killed a woman and seriously wounded three others in Austin early on Sunday when he shot into a crowd leaving nightclubs in the Texas capital's downtown area, police said.

The gunman opened fire at about 2:15 a.m. local time before fleeing, Austin police chief of staff Brian Manley told reporters.

Police in a statement late on Sunday said they were seeking to find a 24-year-old man named Endicott McCray on a felony arrest warrant in connection with the shooting.

The motive for the attack, which occurred just minutes after bars closed, was not immediately clear.

"It was a very chaotic scene," Manley said. He described people emerging from clubs and bars running in all directions at the sound of gunfire, as police officers on patrol rushed to the scene.

The gunman killed a woman in her 20s and wounded three other women, who were transported to a local hospital with injuries that were serious but not life-threatening, Austin-Travis County Emergency Medical Services spokesman Mike Benavides told reporters.

The shooting in the Texas state capital follows several recent major acts of gun violence in the United States.

On June 12, a gunman who sympathized with Islamist extremist groups killed 49 people at a nightclub in Orlando, Florida, in the deadliest mass shooting in modern U.S. history.

On July 7, a U.S. military veteran shot and killed five police officers in Dallas in the deadliest day for U.S. law enforcement since the Sept. 11, 2001, attacks. Just over a week later another gunman killed three officers in Baton Rouge, Louisiana. The attackers in all three incidents were killed by police.

Austin, whose downtown area is known for its lively music scene, has a population of more than 900,000.

(Reporting by Alex Dobuzinskis in Los Angeles; Editing by Catherine Evans and Michael Perry)