PHILADELPHIA — A note expressing hatred for police was found after a man opened fire on a Philadelphia police officer then went on a shooting rampage, injuring a second officer, killing a woman, and wounding three other people before he was killed by police, authorities said Saturday.

Police Commissioner Richard Ross identified the gunman in the Friday overnight attack as Nicholas Glenn, 25, who he said had a criminal record.

Ross said Glenn had a 9mm Ruger and at least three magazines as well as a plastic bag with 13 to 15 live rounds. Investigators were trying to track the origins of the weapon, which had an obliterated serial number.

‘‘Obviously, he was hell-bent on hurting a lot of people,’’ the commissioner said at a news conference, adding that ‘‘we aren’t absolutely clear as to why.’’

The note was addressed ‘‘Doomed People’’ and expressed hatred for law enforcement and a probation officer, Ross said. It was found on the gunman, he said.

Police believe Glenn acted on his own and not as part of a group.

‘‘We know [Glenn] carried out one of the most violent acts that we’ve seen in Philadelphia in a long time,’’ Ross said. ‘‘This rambling suggests that he clearly was trying to target a police officer.’’

The commissioner described the violent events as ‘‘completely bizarre’’ and said he would have no difficulty believing mental illness was involved in Glenn’s actions.

The wild chase and shootout through the streets of Philadelphia began about 11:20 p.m. Friday when Sergeant Sylvia Young, a 19-year police veteran, was ambushed while sitting in her patrol car in west Philadelphia.

Young was shot a number of times in the arm and protective vest, Ross said.

‘‘She didn’t hear him say a word, just walked up on her and started firing,’’ Ross said. ‘‘She did hear about 15 shots or so, and that’s consistent with the scene, where we believe she was struck at least eight times.’’

Officers hearing the shots pursued the gunman, who then fired into a nearby bar, hitting a security guard in the leg, then grabbed a woman and used her as a shield before shooting her in the leg, Ross said.

Moments later, the suspect shot into a car 14 times, hitting a man and a woman in the chest. The 25-year-old woman, who was hit seven times, was pronounced dead just before 2 a.m. Saturday, police said.

Ross said two police officers and University of Pennsylvania police officer Ed Miller chased the man into an alley, where the suspect was shot and killed. Miller was shot in the pelvis and right ankle.

Both Miller, 56, and Young, 46, were in stable condition Saturday at Penn Presbyterian Hospital, as were the three other people hit by gunfire. Police said both officers were in good spirits.

Ross said he was astounded the officers survived the close-range shooting and recalled the Jan. 7 ambush shooting of Officer Jesse Hartnett.

Hartnett was shot and wounded as he sat in his cruiser at an intersection by a man who investigators say told them he was ‘‘following Allah.’’