Rhodes says the gunman is also dead but he did not say how he died.
Hundreds of holiday shoppers and store employees evacuated the mall after the shots rang out around 3:30 p.m. Many others hid in stores, and Rhodes says deputies are going through the mall to get them out.
Kira Rowland told KGW-TV that she was shopping at Macy's with her infant when the shots started.
"All of a sudden you hear two shots, which sounded like balloons popping," Rowland told the station. "Everybody got on the ground. I grabbed the baby from the stroller and got on the ground."
Rowland said she heard people screaming and crying.
"I put the baby back in the stroller and ran like hell," Rowland said. "It was awful. It was shots after shots after shots like a massacre.
"It was just awful."
Holli Bautista, 28, said she was shopping in the Macy's for a Christmas dress for her daughter when she heard a two or three pops that sounded like firecrackers.
"I heard people running and screaming and saying 'Get out, there's somebody shooting,'" she told The Associated Press. "It was a scene of chaos."
She said hundreds of shoppers and mall employees started running, and she and dozens of other people were trying to escape through an exit in the department store.
Bautista said the Macy's opens into the food court area, where it was reported the shootings took place. Bautista said it sounded like the shots were coming from that direction.
Once Bautista made it out of the mall, police officers were directed her and the other shoppers across the street to another shopping center.
As she looked across the street, Bautista said she could see hundreds of police officers, firefighters and emergency workers pouring in.
"They're coming in from multiple different agencies. There's tons of ambulances lined up," she said.
Macy's employees Pam Moore and Austin Patty told the AP the shooter was short, with dark hair, dressed in camouflage. He had body armor and a rifle and was wearing a white mask, they said.
"I heard about 20 shots and everyone hit the ground," Moore said. "That's when we all just ran."