TACOMA, Wash. — Parents of the man most seriously wounded in a shooting rampage at a shopping mall said Tuesday that he drew a pistol and confronted the gunman before being shot.

Brendan “Dan’’ McKown, 38, was hit twice in the abdomen on Sunday, when a gunman opened fire on crowds in the Tacoma Mall.

Doctors at Tacoma General Hospital believe McKown may have suffered permanent paralysis because of spinal damage, hospital spokesman Todd Kelley said.

Tacoma police spokesman Mark Fulghum said detectives don’t know if McKown simply brandished his handgun to show the gunman he was armed, or if he was preparing to fire the weapon. Witnesses told the family McKown was shot after he pulled the gun.

Roger McKown, 63, of Yelm, called his son a hero and said he has been licensed to carry a firearm for years.

“Dan has been one that always believes in protecting other people, and he put his life on the line for other people,’’ he said at a hospital news conference.

The younger McKown has undergone two surgeries and remains on a respirator, the hospital said. He also suffered a superficial gunshot wound to the right elbow.

Dominick Sergio Maldonado, 20, of Tacoma, pleaded not guilty on Monday to assault, kidnapping and firearms charges for Sunday’s shooting. He was held by Pierce County authorities on $2 million bail.

Authorities said Maldonado marched down a mall corridor, firing from an assault rifle and semiautomatic machine pistol before ducking into a store and taking several hostages.

Police said they received a call from Maldonado’s cell phone seconds earlier. The caller told a dispatcher that he planned to start shooting, and said that to find him, police should “just follow the screams.’’

Fulghum said the federal Bureau of Alcohol, Tobacco, Firearms and Explosives was helping detectives trace the history of Maldonado’s weapons.

McKown’s father and stepmother, Beverly McKown, said Brendan encountered the shooter while delivering a bank deposit from the gift store where he works as assistant manager.

“He heard the shooting, and before he could ever take a defensive mode or anything, it was right there,’’ Roger McKown said.

After Brendan McKown was shot, workers from a nearby camera store attended to his wounds as he lay awaiting medical attention for more than an hour, his father said.

Doctors will now try to bring McKown out of an induced coma, and may attempt to remove a ventilator Wednesday, the hospital said. McKown’s mother, Patricia Marush, remained in her son’s hospital room during Tuesday’s news conference.

Five other people have been released after being treated for wounds suffered in the shooting, which broke out about noon Sunday.

Three hostages in a mall music store spent hours talking with the gunman, who described to them a life of frustration and humiliation.

One of the hostages, Joe Hudson, told The Seattle Times that Maldonado spoke of suicide attempts and said he had taken methamphetamine before he started shooting.

Fulghum confirmed that Maldonado demanded to see three police officers from other cities during the hostage negotiations, claiming the officers had humiliated him during a youth summer camp years earlier.

The hostages said Maldonado eventually broke into tears, dismantling his weapons and handing them over to the hostages.

Prosecutors said Maldonado was a felon and had a substantial juvenile record, including burglary.