The officer was identified as Capt. Robert Melton. He was 46 years old and had been with the department for 17 years.
Zeigler told reporters the officer was looking for four people in a car some time before 2 p.m. when the vehicle was spotted and a chase began. The chase ended about 2 miles from where the suspects were initially reported to a 911 dispatcher.
"As Capt. Melton was arriving, the suspects bailed from the vehicle and opened fire," the chief said. "I don't have any more details than that."
Another officer who had just arrived called for assistance, police spokesman Thomas Tomasic said earlier during a briefing at the scene of the shooting.
Tomasic said he knew the officer who had been shot, calling him a "good friend, good person."
One person is in custody and two others who might be connected to the incident have been detained. Police are searching for at least one more suspect, Tomasic said.
A police statement said the Melton family had asked for the media to give them privacy.
Kansas City Mayor Mark Holland asked for people not to jump to conclusions and wait for an investigation to answer why the officer was killed.
"We just want to ask for the thoughts and prayers for Capt. Melton's family and for our entire police department right now and for our community," Holland said at the hospital. "There's a lot of pain and brokenness in our community and our nation right now and we just want to ask everyone to be prayerful and thoughtful."
Dr. James Howard of the University of Kansas Hospital said Melton had no blood pressure or pulse when he arrived. Doctors and nurses at the University of Kansas Hospital tried for 30 minutes to revive Melton before he was pronounced dead.
The death is the second for the department in two months. Det. Brad Lancaster was shot and killed May 9
while trying to apprehend a carjacking suspect.
A total of 31 law enforcement officers have been shot to death while on duty this year, according to the Officer Down Memorial Page. Six K-9 officers also have been fatally shot.
Nine other K-9 officers have died of heat exhaustion, including Mojo, an Arlington, Texas, police dog that died Tuesday after overheating during pursuit of a fugitive