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Four people are dead, including the gunman, after a shooting at a bank in the United States city of Cincinnati.

Witnesses said they heard volleys of gunfire and one said that a woman was shot as she entered the bank building's lobby.

Omar Perez, 29, acted alone when he opened fire at the headquarters for the Fifth Third Bank near the Fountain Square, Cincinnati Police Chief Eliot Isaac said in a press conference Thursday afternoon.

Chief Isaac says the suspect was engaged by several officers.

Perez. of Northbend, Ohio, is not a former or current employee of the bank, Isaac said.

The situation appeared to be under control shortly before 10 a.m. EDT Thursday but police said they are still investigating. The shooter is dead along with three of his victims.

One victim was at a Graeter's ice cream shop in the area while another was 5th and Walnut streets, the Enquirer reported. Police also found "multiple magazines" and about "200 rounds of ammunition" on Perez. "It could have been any one of us", he said.

Emergency personnel and police responded to reports of an active shooter situation near Fountain Square, today, in downtown Cincinnati. This is abnormal. No other industrialised country has this level of active multiple shooting on a regular basis... Yudy Martinez Perez broke down in sobs when she learned her nephew was the shooter, the Cincinnati Enquirer reported.

"It's heartbreaking", Cranley said.

Federal agents were on the scene as police searched through the building. Eastern time, none of the victims had been publicly identified. In all, the hospital received four gunshot wound victims from this morning's incident.

It is understood that three or four officers responded nearly immediately. One is in critical condition and one is serious.

Confirming the gunman died in the shootout, he added: "The shooter is deceased".

Michael Richardson, who works in the bank building, told The Cincinnati Enquirer that he was standing outside the entrance when he heard gunshots in the lobby.

"Everybody was in there crying".

"Then we knew what was going on", Hanson said. "We just saw glass and everything flying".

Sammarco posted Wednesday on Facebook, asking how officials will explain to his parents "they will never see their son again because of a senseless shooting in a foreign country". Passersby tried to similarly warn a woman not to enter the building, but she couldn't hear them over her headphones.

"I kind of got down on the ground and then all the cops started coming", he said.

Cranley said the shooting "could have been much, much worse" if not for an immediate police response.

Carla Herreria contributed reporting. We have more details here.