An Oakland, California, police officer critically injured in one of two Saturday shootings that killed three fellow officers was pronounced brain dead on Sunday, a police spokesman told CNN.

Initially, Oakland police spokesman Jeff Thomason said John Hege, 41, was the fourth officer to die after a man being pulled over in a traffic stop opened fire and then battled SWAT officers at a nearby building Saturday.

However, Thomason clarified later Sunday that Hege was pronounced brain dead about noon Sunday, but being kept on life support until a decision is made on organ donation.

The man who police said was the gunman -- Lovelle Mixon, 26, of Oakland -- was fatally shot in a gunbattle with SWAT officers in an apartment complex Saturday.

Police said in a late-night news conference Saturday that Mixon had an extensive criminal history and was in violation of parole for assault with a deadly weapon. He also had prior convictions in Alameda County for grand theft and possession of marijuana, the Oakland Tribune newspaper reported. The city of Oakland is in Alameda County.

The incident began about 1 p.m. Saturday in east Oakland when two motorcycle officers tried to pull over a car for a "fairly routine traffic stop," said Dave Kozicki, the deputy police chief.

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photo: Clockwise from top left: John Hege, Sgt. Daniel Sakai, Sgt. Ervin Romans and Sgt. Mark Dunakin (Oakland Police Dept via Getty Images)