National prison police director Luis Masferrer said the blaze broke out at about 5:30 a.m. (7:30 a.m. EST; 1230 GMT) at the San Miguel prison south of the capital, and it was brought under control three hours later.
Chile's health minister, Jaime Manalich, called it an "enormous calamity," "probably the worst in the history of our penitentiary system."
Hundreds of anxious and angry relatives of inmates gathered in a chaotic scene outside the prison gates. Some told state television that prison police initially closed the gates to firefighters, impeding efforts by 10 responding units to control the blaze.
Police operations director Jaime Concha insisted police acted quickly despite coping with 1,900 inmates at the prison built for 700.
Pedro Hernandez, who directs Chile's prison guards union, said there were only five guards to watch over the prisoners. Pinera, however, said there were six guards in the prison towers where the inmates are held, and 26 others stationed at the perimeter.
Chile's firefighters said in an official statement that they were alerted to the fire by a call from a cell phone inside the prison. The release didn't say whether it was a prisoner or guard who called.
Authorities have not said why so many inmates died or how long it took firefighters to enter the part of the prison where the blaze began, on the third floor of Tower 5. Firefighters had to work with police to avoid more problems with prisoners all around them.
"They wouldn't let the firefighters come in. The riot police came in first and began to beat us, and later the firefighters came in," an unidentified prisoner said in a call that was played on state television.
While more than 200 inmates were moved to other areas of the prison, there were 147 others in the immediate area of the blaze, and many died of asphyxiation, the firefighters' statement said.
It was supposed to be visitors' day at the prison, so many family members were already lining up outside when the fire broke out. Their anxiety spilled over when they learned that prisoners were killed. Some broke down in tears and screams, while others threw rocks at Masferrer, the prison police director, as he read the survivors' names over a megaphone.
Manalich said 14 prisoners were badly burned, with uncertain fates. Two firefighters and three guards were less seriously hurt, authorities said.