A lone gunman has opened fire at a major university in Florida, wounding three students before being shot dead by police, officials say.

The latest episode of America's epidemic of gun violence happened early on Thursday morning at Florida State University in the capital city Tallahassee.

More than 300 students were in the university's Strozier Library when several shots rang out.

Officers responding to reports of gunfire confronted the gunman outside the library and shot him after he refused an order to put down his pistol, Tallahassee city police spokesman David Northway said.

Some witnesses said the gunman was shot 30 to 40 times.

Of the three students who were shot, two were in hospital, one in critical condition, healthcare officials said. A third was treated at the scene.

Northway said an investigation into the motive of the shooting was underway. The gunman's identity was not immediately disclosed.

Florida State University president John Thrasher, in a statement, said investigators assured him that the shooting was "an isolated incident."

"Security is not lacking on campus," added Florida State University police chief David Perry.

"This person for whatever reason produced a handgun and started shooting."

Classes were cancelled on Thursday, but the university - with more than 40,000 students - remained otherwise open.

Students told US media that as many as four shots had been fired within the library.

One student, Sean Young, told local television channel WCTV he was on the third floor when students started running frantically past him, and someone said a gunman was downstairs.

With a fellow member of his fraternity, Young crammed as many people as possible into a study break room, hoping they would all be safe inside.

"I just tried to remain calm, especially for those that were around me. I didn't want to panic anybody else. For me personally, it's still kind of registering," he said.