Two people are dead and six others are in hospital after a shooting on Thursday at Florida State University in Tallahassee.

The deceased were not students, campus police said, but their identities have not been released.

The alleged gunman was identified as 20-year-old FSU student Phoenix Ikner, Leon County Sheriff Walter McNeil said. Mr Ikner also was shot by police and is in hospital.

Mr McNeil said he is the son of a Leon deputy and one of the guns found at the scene is a former service weapon purchased by the gunman's mother, Jessica Ikner, a school resource office on the force for 18 years.

The university has cancelled all classes until at least Friday, and sports events were also cancelled for the weekend.

Police responded to an active shooter call at around midday local time, the university said. An alert was issued soon after, warning students and those on campus to "seek shelter and await further instructions".

"One of my classmates got an alert on her phone and announced it to the rest of the class," student Ava Arenado told CBS News Miami.

Another student, Blake Leonard, told CBS that he initially heard roughly 12 shots fired.

"In my head, I thought it was construction at first, until I looked behind me and saw people running from the union towards my direction, and then I heard another 12 or 15 shots go off, so I started running away from there too," he said.

President Donald Trump, who said he was briefed on the incident before meeting with Italian Prime Minister Giorgia Meloni at the White House, was asked whether he wanted to change gun regulations in light of the shooting.

"I'm a big advocate of the Second Amendment. I have been since the beginning. I have protected it. These things are terrible," he responded. "We will have more to say about it later."

He called the shooting "a shame, a horrible thing".

Florida Governor Ron DeSantis said: "Our prayers are with our FSU family and state law enforcement is actively responding."

This is not the first shooting at Florida State University. In 2015, a graduate of the school shot and injured three people at the library before he was fatally shot by police.