It remained unclear whether the parking lot shootout and the standoff at the restaurant were connected, and authorities were continuing to search the Chandler Fashion Center to make sure that only one suspect was involved in both incidents, officials said.
Hundreds of mall patrons and employees were evacuated but an unknown number remained inside as police searched "every nook and cranny" of the mall, Chandler police Sgt. Joe Favazzo said.
There were no reported injuries.
The first burst of gunfire erupted just outside an entrance to a Sears store when members of a U.S. Marshals Service fugitive task force confronted a man they believed to have committed several robberies in recent days in the suburbs east of Phoenix, Arizona Department of Public Safety spokesman Bart Graves said.
The suspect also was believed to have been the same man who shot at DPS officers in Casa Grande, south of Phoenix, on Dec. 10, and was wounded by return fire, then mistakenly released from custody late last month.
However, authorities later said they could not confirm if the suspect involved in the shooting Wednesday was the Casa Grande suspect.
The man who surrendered after the standoff at the fast food restaurant was not the suspect in the Dec. 10 shooting.
When the gunfire erupted outside the mall, shoppers and employees inside ran in all directions trying to get out of the way.
Tuan Tang, an Iraq war veteran working at the mall food court, said security officers began calling for people to evacuate and he relied on his Army training to help usher customers outside.
"It helped me handle the situation and evacuate the people, Tang said.
Witness Katie Corbin, who was inside Chandler Fashion Center at the time of the midday shooting, told KTVK-TV that people went to the back of the Victoria's Secret store after shots were fired. The upscale shopping center includes a Banana Republic, Coach, Nordstrom and other stores.
She said the situation inside the mall was "scary."
Shoppers and employees of stores and restaurants waited outside the mall on a street, and state police officers blocked access to the mall.
December Davis, 22, a waitress at the Kona Grill inside the mall, said she and others were told to drop everything and exit the shopping center. People left without their purses, cell phones and other belongings.
Witness Michael Bayne told KPHO-TV he saw police running by a kiosk inside the mall and heard gunshots.
Bayne said police told mall patrons and employees to leave the mall. The mall was then placed on lockdown.