A gunman opened fire at a bank building in the US city of Cincinnati yesterday, fatally wounding three people before police shot and killed him, authorities said.

The incident occurred after 9:00 am local time (1300 GMT) at the lobby and loading dock of the 30-story Fifth Third Bank building in the city's downtown business district.

"An individual entered the loading dock area, began firing shots," Cincinnati Police Chief Eliot Isaac said at a news conference.

The gunman then went to the lobby of the building, where police engaged the suspect in a shootout and killed him, the chief said.

"At least three or four of our officers did engage the suspect," Isaac said.

Three people died of their wounds and two others remained hospitalized.

The shooter's identity or motive were not released.

Cincinnati Mayor John Cranley said the shooting could have been "much worse," had it not been for the quick response of police officers in the area.

"He was actively shooting innocent victims it appears," Cranley said. "Police were there within seconds, literally."

One unnamed eyewitness, a construction worker, told WLWT television that he heard at least six gunshots before police arrived.

"I just seen people running out of the building," the eyewitness said.

"There's guys with suits laying on the ground, hiding behind big flower pots," he said.

The office tower where the shooting occurred remained on lockdown more than an hour after the incident, as police swept the building.

Police cordoned off a portion of the city's downtown.

"There was a senseless act of gun violence on the streets of Cincinnati this morning," Ohio Governor John Kasich said on Twitter.

"I commend the law enforcement, fire and (emergency medical) personnel who swiftly responded to the scene and share my deepest sympathies with the innocent victims of this violent attack."