Walker was pronounced dead at 1:49 p.m. at the Medical Center of Central Georgia.
"This is a terrible tragedy," Jones said, adding that he didn't know any more about the circumstances of the mayor's death, including where he died. "We need to keep the Walker family and this community in our prayers."
"He's a very good friend, a longtime friend. I'm shocked and I'm stunned by what I've heard. I just can't believe what I've heard," said Jim Worrall, who has been mayor of neighboring Perry for 21 years and said he'd always admired Walker's leadership.
"I thought he was one of the most progressive visionaries that we've had around here in a real long time," he said. "He saw how Warner Robins could be a home, truly a city, and not just a place where there's an air base."
Warner Robins is home to Robins Air Force base, which is the largest industrial complex in Georgia, employing more than 25,500 civilians, contractors and members of the military.
Walker, 60, was in the middle of a competitive re-election campaign.
He was first elected in a special election in 1994. He won re-election in 1997 with more than 85 percent of the vote. State Rep. Pam Bohannon challenged him in 2001, but he won with 64 percent of the vote. He ran unopposed in 2005.
Walker was a native of Warner Robins. The city's Homer J. Walker Municipal Complex is named after his father, who was mayor of the city from 1968 to 1972.
During his term, Walker focused on the growth of the city through annexation and attracting business and industry, according to the city's Web site.