A man armed with a rifle and a handgun killed four people inside a medical building in Tulsa, Oklahoma on Wednesday before fatally shooting himself, police said, in the latest of a series of mass shootings to rattle the United States.

Police arrived at the St Francis Hospital campus three minutes after receiving a call about the shooting on Wednesday afternoon and followed the sound of gunfire up to the Natalie Building's second floor, Tulsa deputy police chief Eric Dalgleish told reporters.

The officers made contact with the victims and the suspect five minutes later, Dalgleish said.

Police responses have come under increased scrutiny after a gunman killed 19 children and two teachers in a Texas school classroom last week while officers waited outside for nearly an hour.

Asked by reporters whether police had refreshed training or thinking about active shooters after the Uvalde, Texas school shooting, Dalgleish said: "I think that's probably fresh on everyone's minds."

"I will say Tulsa revisits that topic regularly. I was very happy with what we know so far regarding the response of our officers," Dalgleish said.

Wednesday's incident in Tulsa came on the heels of mass shootings that have reignited debates about gun control. Two weeks before the Uvalde shooting, a white gunman killed 10 people at a supermarket in a Black neighbourhood in Buffalo, New York.

Police in Tulsa said they were trying to determine the suspect's identity, who they estimated was aged between 35 and 40, and had no details yet on his motive.

The Natalie Building contains doctors' offices including an orthopaedic centre, Dalgleish said, adding he believed the victims included employees and patients.

The White House said President Joe Biden had been briefed on the shooting and offered support to state and local officials in Tulsa, a city of some 411,000 people that sits around 100 miles (160 km) northeast of the capital Oklahoma City.