One of the larger pieces hit the agent in the head and that the agent feared for his life, investigators said.
Flores Cruz suffered two gunshot wounds, the sheriff's department said in a press release. Authorities said they confirmed his identity with a fingerprint match from a 1996 arrest by the U.S. Drug Enforcement Administration. No further details on that arrest were released.
Under current policy, agents can use deadly force if they have a reasonable belief that their lives or the lives of others are in danger. The Border Patrol has long maintained rocks can be lethal weapons.
The Police Executive Research Forum, a nonprofit group that led a government-commissioned review, previously recommended that the Border Patrol and its parent agency, Customs and Border Protection, prohibit deadly force against rock-throwers and assailants in vehicles, Border Patrol Chief Mike Fisher said last year.
Customs and Border Protection rejected the proposed curbs, which Fisher called "very restrictive."
Agents were attacked with rocks 339 times in the 2011 fiscal year, more than any other type of assault, according to the Department of Homeland Security inspector general. They responded with gunfire 33 times and with less-than-lethal force a category that includes pepper spray and batons 118 times.
Rock attacks fell to 185 instances in fiscal 2012, becoming the second-most-common type of assault. Agents fired guns 22 times and responded 42 times with less-than-lethal force.
Department of Homeland Security Deputy Secretary Alejandro Mayorkas didn't address specifics when asked about the shooting Wednesday but said the Border Patrol's use-of-force policy would be publicly released.
"We are committed to ensuring the safety of our men and women who put their lives on the line on the border," he said. "At the same time we are committed to ensuring that our use-of-force policies are a reflection of best practices."
Associated Press writer Christopher Sherman in Mission, Texas, contributed to this report.