The area has been cordoned off, police said.
They were identified as Prudhvi Raj Kandepi, 25, Richard Newcomer, 64, and Luis Felipe Calderón, 48, according to the Hamilton County Coroner's office.
Emergency officials rushed four more victims to a local hospital, where two were later pronounced dead.
One of the victims died at the scene.
Local police said the gunman opened fire at the loading dock of the building and then entered the bank's lobby where he exchanged gunfire with police.
Perez was allegedly armed with a 9-millimeter pistol, multiple magazines and about 200 rounds of ammo.
Tropical Storm Gordon's remnants move into Arkansas; heavy rain, severe storms possible
The rain will start to slowly taper off Monday mid afternoon, but still scattered showers expected through Tuesday morning. In addition to widespread heavier rainfall locally, excessive rain to our north has resulted in higher river levels.
Santa Perez is also believed to have been living in the Greater Cincinnati area since at least 2015.
He was not a current or former employee at the center, whose primary tenant is the Fifth Third Bank headquarters, and officials say they are not sure of his connection with any surrounding businesses.
"There may be a possibility that there's some mental health issues involved here", Cincinnati police chief Eliot Isaac told a news conference, cautioning that the investigation was in its early stages.
Another employee, Michele Parks said she was about to go into the bank when Cook stopped her.
Steve Conner lives on the first floor of the apartment building where the Santa Perez lived.
Thursday's incident is the second this year where an Indian was shot dead in the US.
He then made his way to the lobby, where he was met by police officers who gunned him down.
Prescription Painkiller Boosts Risk of Heart Attack, Stroke
However, researchers point out that, while the relative risk increased significantly, the overall risk was still pretty small. The researchers' paper is titled, " Diclofenac use and cardiovascular risks: series of nationwide cohort studies".
-This report was updated at 11:38 a.m.
A visitor from Germany sat at a table on Fountain Square, enjoying a sunny morning when he heard some teens shouting about a shooting.
The evidence includes footage from body police cameras and security cameras from around Fountain Square and Fifth Third Center. "You know, these are things that we see happening across the country, and we all have to be vigilant and prepared to deal with these situations". "We're a bit rattled".
Another witness told FOX19 that he thought there was movie filming until he saw police carrying a wounded woman away from the scene and saw officers rushing to the scene.
Five people were shot, some multiple times, in the incident, they said, adding that the gunman was killed in a shootout with the police. The FBI and ATF also assisted.
Mayor John Cranley called the police and fire rescue response "heroic".
In the family statement, Whitney Austin said she is still processing events and the impact of the shooting to all the victims and the community.
Novak Djokovic expresses frustration with team during match
Mini-breaks were aplenty - seven in total - and it was Nishikori's mind games which tricked Cilic into surrendering the set. The win meant that Djokovic advanced to his 11th straight U.S. semifinal - a streak only bettered by Jimmy Connors.