Perez killed three people and wpounded two before he was shot dead by police, Isacc said.
The suspect, Omar Enrique Santa Perez, had a pistol and more than 200 rounds of ammunition, police said. Two others are injured and in critical condition.
Mayor Cranley said a vigil is planned for 4 p.m. on Friday for victims, first responders and the city.
He noted the building on the city's Fountain Square houses popular ice cream, sandwich and pastry shops.
Al Jazeera contacted the Cincinatti Police Department but did not immediately receive a response.
Cincinnati police chief Eliot Isaac said investigators don't know why Santa Perez made a decision to open fire in the building where Fifth Third Bancorp has its headquarters.
The Cincinnati Enquirer reports Yudy Martinez Perez slumped against a kitchen wall and muttered denials after she heard the news.
Witness Cheryl Eagleson said she was across the street from the bank when she heard "loud pops" from a gun, prompting people to drop to the ground.
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A witness said he heard up to 15 shots.
Yudy Martinez Perez broke down in sobs when she learned her nephew was the shooter, the Cincinnati Enquirer reported. Police said that the situation was under control shortly before 10:00am ET, but they are still investigating.
There were people screaming "shooter, run, leave", in Fountain Square, a park that often hosts concerts, dancing, and food trucks. "It could have been any one of us", he said.
"I looked behind me and saw the guy - he shot and then he shot again", Richardson said.
The area around the bank was closed to pedestrians after the shooting, police said.
Perez. of Northbend, Ohio, is not a former or current employee of the bank, Isaac said.
A police officer comforts a woman outside UCMC ER following an active shooter situation in downtown Cincinnati.
A large police presence cordoned off a portion of the city's downtown, and several ambulances could be seen at the scene. She said the gunman was so close she could smell the gunpowder as he fired. "Then he saw a man in white shirt and brown trousers holding a gun and heard 'rounds of gunfire, '" he wrote. "We didn't know where to go because we didn't have a backdoor", she told reporters.
Police earlier characterized the incident as an "active shooter/officer involved shooting incident" in a tweet but did not elaborate. The Fifth Third Center is a 30-story skyscraper that sits on the square.