“This is a different type of active shooter that we were involved with, because he was mobile, and that creates some very special type of issues,” Chief Gerke said.

The gunman sped away from the state troopers who had tried to pull him over, and then hijacked a United States Postal Service van, killed its driver, and began firing at people randomly as he drove. In cellphone video from witnesses that captured the final moments of the shooting spree, the postal van speeds into view and slams into a police cruiser outside the movie theater in Odessa. A burst of gunfire followed as officers who had been chasing the van rushed out and shot the gunman, who appeared to still be inside the van.

The authorities said Sunday that the seven people killed in the attack ranged in age from 15 to 57, including Mary Granados, 29, the driver of the postal van. The Postal Inspection Service said Ms. Granados was a letter carrier, that it was “shocked and saddened” at her death, and that it was working closely with other agencies on the investigation.

A total of 22 people were wounded, officials said, including three law enforcement officers and a 17-month-old toddler who was recovering Sunday from injuries that included shrapnel in her chest.

The attack on Saturday spread panic and fear for hours across West Texas, hundreds of miles from the border city of El Paso, where four weeks earlier a gunman had killed 22 people at a Walmart in an anti-Hispanic attack.

On Sunday afternoon, federal agents executed a search warrant at what appeared to be Mr. Ator’s residence, in a remote area of mobile homes at the western edge of Ector County, which includes Odessa. A neighbor, Rocio Martinez, 29, described Mr. Ator as a “loner” who kept to himself and who sometimes frightened her because he was always firing guns outside.