A gunman carrying a rifle and a handgun has killed four people at a medical building on a hospital campus in Tulsa, Oklahoma.

The incident at the Natalie Medical Building on the St Francis Hospital campus is the latest in a series of deadly mass shootings across America in recent weeks.

Tulsa police department deputy chief Eric Dalgleish confirmed the number of dead and said the shooter is also dead, apparently from a self-inflicted gunshot wound.

The spate of recent gun violence across the US, including the killing of 19 children and two teachers at a Texas elementary school eight days ago by an 18-year-old gunman carrying an AR-style semi-automatic rifle, has led to Democratic leaders amplifying their calls for greater restrictions on guns, while Republicans are emphasising more security at schools.

The divide mirrors a partisan split that has stymied action in US congress and many state capitols over how best to respond to a record-high number of gun-related deaths in the US.

It was unclear what prompted the deadly assault in Tulsa, Mr Dalgleish said.

"It appears both weapons at one point or another were fired on the scene," Mr Dalgleish said.

"The officers who arrived were hearing shots in the building, and that's what led them to the second floor."

Police responded to the call about three minutes after dispatchers received the report at 4.52pm (10.52pm BST) and made contact with the gunman roughly five minutes later, at 5.01pm (11.01pm BST) Mr Dalgleish said.

"I was very happy with what we know so far regarding the response of our officers," Mr Dalgleish said.

The length of time it took police officers in Uvalde, Texas, to engage the gunman during last week's deadly shooting at Robb Elementary School has become a key focus of that investigation.

Officers waited over an hour to breach the classroom where the gunman attacked.

Police captain Richard Meulenberg also said multiple people were wounded and that the medical complex was a "catastrophic scene". The exact number of wounded was not immediately available.

Police and hospital officials said they were not ready to identify the dead.

St Francis Health System locked down its campus on Wednesday afternoon because of the situation at the Natalie Medical Building.

The Natalie building houses an outpatient surgery centre and a breast health centre.

Mr Dalgleish said an orthopaedic clinic is also located on the second floor where officers discovered the shooter and several victims.

"This campus is sacred ground for our community," said Tulsa mayor GT Bynum.

"For decades, this campus has been a place where heroes come to work every day to save the lives of people in our community.

"Right now, my thoughts are with the victims. If we want to have a policy discussion, that is something to be had in the future, but not tonight."

Agents from the Bureau of Alcohol, Tobacco, Firearms and Explosives were also at the scene, a spokesperson said.

A reunification centre for families to find their loved ones was set up at a nearby high school.

The shooting Wednesday also comes just more than two weeks after shooting at a Buffalo supermarket by a white man who is accused of killing 10 black people in a racist attack.

America's recent Memorial Day weekend saw multiple mass shootings nationwide, including at an outdoor festival in Taft, Oklahoma, 45 miles from Tulsa, even as single-death incidents accounted for most gun fatalities.

Since January, there have been 12 shootings across the US where four or more people have been killed, according to The Associated Press/USA TODAY/Northeastern University mass killing database.

Those shootings have left 76 dead, including 31 adults and children in Buffalo and Texas, the database says. The death toll does not include the suspects in the shootings.