Crist's comments came hours after prosecutors released an enhanced video of the beating of Martin Lee Anderson, 14, and more than 20,000 pages of evidence in the in the manslaughter case against seven former guards and a nurse.
The family had sued for $40 million, but said in a letter to Crist that a $10 million payment would be a fair resolution — half from the state and half from Bay County, which ran the camp.
"I think it's real important that the state do the right thing, and I think the right thing to do is honor their more-than-reasonable request. Justice delayed is justice denied," Crist said in Tallahassee. The payment would have to be approved by the Legislature.
"We just think it's very courageous that he would take the leadership and go forward to get a resolution," said Benjamin Crump, the family's attorney. The family will still pursue payment from Bay County.
The newly released material included a NASA-enhanced video that more clearly shows the guards striking Anderson with fists, pinning him down and holding what appears to be a white cloth to his face at the now-closed sheriff's boot camp in Panama City.
Investigative reports said the nurse examined him early in the incident and said his vital signs were normal. The tape shows her watching, but she does not appear to give another close examination until about 27 minutes into the tape. At that point, guards have stopped hitting him.
Paramedics arrive about 35 minutes into the tape and load the teen onto a stretcher. He died in a Pensacola hospital the next day, starting a case that led to the dismantling of Florida's military-style detention system for young offenders and protests at the state Capitol.
An initial autopsy found Anderson died of natural complications of sickle cell trait, a usually benign blood disorder. But after an uproar and cries of a cover-up from the boy's family, a second autopsy was conducted by another medical examiner, who concluded Anderson was suffocated by the guards' hands over his mouth and the "forced inhalation of ammonia fumes."
Anderson collapsed at the camp while doing exercises. The guards said they were trying to revive him, but his family and others were outraged at the video footage.
The guards and the nurse pleaded not guilty last month. They face up to 30 years in prison if convicted of aggravated manslaughter.