A man who went on a rampage at a Texas outlet mall on Saturday shot dead eight people before he was himself killed, authorities said.

"(We) found seven deceased individuals on scene. We transported nine individuals to the hospital... Of those we transported, two have since died," said fire chief Jonathan Boyd of Allen, Texas.

The shooting sparked panic at Allen Premium Outlets, a sprawling shopping complex in Allen, 25 miles (40 kilometers) north of Dallas, filled with weekend shoppers.

A police officer was in the mall on an unrelated call when gunfire broke out around 3:30 pm (2030 GMT), said chief Brian Harvey of the Allen police department.

"He heard gunshots, went to the gunshots, engaged the suspect and neutralized the suspect," Harvey said. "He also then called for ambulances."

The identity of the shooter was not released. His body, sprawled on a sidewalk, was one of the seven deaths at the mall when more police arrived.

Among the wounded at area hospitals, "three are in critical surgery, and four are stable," Boyd, the fire chief, said.

Some of the victims were as young as five years old, a hospital official told NBC News.

Texas Governor Greg Abbott called the mass shooting an "unspeakable tragedy."

President Joe Biden "has been briefed on the shooting," a White House official told reporters.

Local officials hailed the actions of the police officer who charged and killed the shooter.

"We owe a debt of gratitude to first responders that ran toward the gunfire and acted swiftly to neutralize the threat," said Keith Self, a Republican congressman whose district includes the city of Allen.

Video footage aired by CNN showed the shooter getting out of a sedan in the parking lot of the mall, and beginning his rampage.

Authorities believed initially that a second shooter might be on the loose. As police combed through stores in the mall, frantic shoppers and store employees rushed into parking lots.

Harvey later said police believe the unidentified shooter, who CNN said was wearing tactical gear, "acted alone."

Janet St. James, a spokesperson for Medical City Healthcare, which operates multiple trauma facilities in North Texas, said it received eight patients from the shooting, ranging in age from five to 61, NBC News reported.

A father who arrived at the mall after his daughter, who was inside, phoned to tell him about the shooting, also told CNN that police had informed him there may have been a second shooter.

"We saw the police outside the door, and they told us we had to go, and that they are still looking for the person," Jaynal Pervez said, according to CNN.

"There's no more safe places. I don't know what to do."

Pervez later told broadcaster CBS that scenes in the mall parking lot were chaotic.

"I saw the shoes around there, people's cell phones on the street," he said.

With more firearms than inhabitants, the United States has the highest rate of gun deaths of any developed country -- 49,000 in 2021, up from 45,000 the year before.

There have been more than 195 mass shootings -- defined as four or more people wounded or killed -- so far this year in the United States, according to the Gun Violence Archive.