A man in Hawaii shot and wounded a woman, stole a car at gunpoint and was later killed in a shootout with police that left two officers wounded, authorities said.

Police began searching for the man Monday, on New Year's Day, after a woman said he shot her, Honolulu Police Chief Arthur "Joe" Logan said at a news conference. The man shot at officers at three different locations before officers shot him near the University of Hawaii’s main campus in Honolulu about 4 p.m., Logan said.

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The man was taken to a hospital, where he died, the police chief said. Two wounded officers underwent surgery Monday. Their conditions were not immediately known Tuesday.

The officers "were shot while attempting to apprehend a dangerous attempted murder suspect," Robert Cavaco, president of the Hawaii police union said in a statement Monday. "We are praying for the full and swift recovery of our injured brothers who risked their lives and sacrificed their safety today to protect the lives and safety of the public."

A fourth man was injured by a police vehicle, Logan said, adding that police were trying to determine if he was involved.

Asked why police didn't notify the public about the ongoing pursuit, Logan replied, "We just needed to focus on apprehending the individual." He added that he didn't want people trying to get involved in the chase.

"It was fluid, it was ongoing and it moved from place to place rapidly," Logan said.