The man reportedly called the Police Department and sounded distraught as he stated he was going to kill himself and a police officer and indicated he may have already killed an officer, police said.
After several more threateningly calls, officers were able to track down where he lived and found the man in his garage in the 4800 block of Lefebvre Way around 3:45 p.m., police said.
The man was standing in his driveway holding a gun, which officers ask him to put down, police said.
He responded by firing at least one round at the officers, who then fired backed at the man, according to police.
He was struck by the gunfire and killed, police said.
The Contra Costa County District Attorney's Office is conducting a joint investigation with Antioch police, as per protocol.