Police said they shot Jairo Bustos, 25, after he rammed an officer's vehicle and tried to run him over in the northern Atlanta suburb of Roswell.
Officers found Bustos in a parking lot after a nearby driver saw an Amber Alert describing the vehicle and called police, said Lt. James McGee, the city's police spokesman.
McGhee said the two children -- a 9-month-old and a 22-month-old -- were strapped in their carseats in the back of the car when the officer shot Bustos. He was unsure whether the car was in motion at the time of the shooting.
The episode unfolded after the children's mother, 22-year-old Adrian Stearns, called police Thursday to say Bustos had taken off with them in her 1994 Honda Accord. Bustos had recently been evicted from Stearns' apartment, said Gwinnett County Police spokeswoman Cpl. Illana Spellman.
A child abduction alert was issued and a motorist spotted a car matching the description on a busy north Atlanta highway on Friday morning, said McGee. Police soon found the car in a parking space at an apartment complex, near where the children's maternal grandparents live, said McGee.
"It went downhill from there," he said.