"There doesn't appear to be any other weapon present than the rock," Dallas Police Assistant Chief Randall Blakenbaker said.
Video posted by Instagram user @flashyfilms and credited to Bryan Armstrong shows people scattering on the sidewalk outside the baggage claim door at Dallas Love Field.
An officer in a yellow vest is seen pointing his gun, and at least nine gunshots can be heard. A man repeatedly yells "stand down!" and a woman is heard screaming.
Some airport operations were temporarily disrupted, but the airport remained open. Spokesman Jose Torres said that some people after hearing shots ran through security so everyone had to be rescreened. Officials warned that delays could last several hours.
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"There were some folks in the security line who were startled, so they went through the security line without being checked. So the airport has had to pull everybody back out of the secure area and recheck them for security purposes," Blankenship said.
Traveler Lucinda Fonseca told WFAA-TV that she and her husband were coming out of the baggage claim area when they saw police approaching the man throwing rocks and one of the officers drew a gun.
"The man was yelling at the cops, basically saying 'shoot me shoot me, I dare you,' something to that effect," Fonseca said, adding she then heard gunfire.
"I crouched down on the ground," she said. "I didn't know where the bullets were going."
Blankenbaker said it appeared that the man had used a large rock from nearby landscaping to smash the windshield and driver's side window of a car. Blankenbaker said no children were present during the disturbance and the woman wasn't injured.