A man in the US state of Florida fatally shot four children before turning the gun on himself after a 21-hour standoff, police say.

Police found Gary Wayne Lindsey Jr, 35, dead in the apartment where he had held the children - aged one to 12 - hostage in Orlando.

Lindsey was the father of two of the children. He was a felon on probation for arson among other charges.

His girlfriend had called police after he battered her during an argument.

A family lawyer identified the four children killed: Iraya, 12, Lillia, 10, Aidan, six, and Dove, one.

In a news conference on Monday, Orlando Police Chief John Mina called it "a very tragic and sad ending".

Chief Mina said it was not clear when the children were killed.

Swat officers entered the apartment on Monday night.

They "found that all four children had been killed by the suspect by apparent gunshot wounds and it appears the suspect took his own life as well," Chief Mina said.

"Our hearts go out to all the families involved."

Police said at least one child was dead when officers attempted to give Lindsey a phone to communicate with police negotiators.

An officer who had been injured in the initial confrontation with Lindsey, Kevin Valencia, remains in a critical condition, the police chief said.

According to court records, Lindsey had been arrested several times over 15 years.

In 2012, he was held for aggravated assault with a deadly weapon, aggravated battery in a domestic violence case and violating his probation.

Police have not released further information about the victims.

How did the standoff unfold?
On Sunday night, Orlando police received a call from a woman who said Lindsey was her boyfriend and that he had battered her during an argument.

She had fled the apartment after he attacked her and called police from a nearby restaurant, the Orlando Sentinel reported.

When officers arrived at the apartment, Lindsey opened fire.

Officer Valencia was seriously injured during the shootout and sent to hospital in critical condition.

Lindsey barricaded himself in the apartment with the four children.

Police negotiators spoke to him several times during what would become a 21-hour standoff.

When they attempted to give Lindsey a better phone to communicate with, police noted one of the children was already dead.

Swat officers entered the apartment shortly after and discovered that all the children had been killed.

They found Lindsey dead in a closet.