Officials said the fire was deliberately started during an early-morning fight between inmates in one of the prison's five towers. Television footage showed part of the San Miguel prison south of the capital in flames, with black smoke billowing from the building.
Frantic relatives of the inmates flooded to the jail's walls, imploring police to let them in to rescue their loved ones.
"It is a hugely painful tragedy," president Sebastian Pinera said, confirming the death toll had risen to 83. "We cannot guarantee the number of dead will not rise."
"We cannot keep living with a prison system which is absolutely inhumane," he added, citing chronic overcrowding in the country's jails. "We are going to speed up the process to ensure our country has a humane, dignified prison system that befits a civilised country."
Pinera said it was the third worst fire Chile has ever suffered. It is also the latest in a string of disasters and accidents to hit Chile this year, including a devastating February earthquake and ensuing tsunamis and a mine collapse that ultimately saw a happy ending when 33 miners were rescued after two months below ground.
Justice minister Felipe Bulnes said the prison housed 1,960 inmates, far over the 700 inmate capacity.
Pedro Hernandez, who directs Chile's prison guards union, said there were only five guards to watch over the prisoners.
Authorities have not said why so many inmates died in 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.
Fire department commander Jose Sanchez said it took ten minutes for firefighters to enter the prison, but he blamed any delay on "the intense heat on the floor where the fire was" rather than on guards.
It was supposed to be visitors' day at the prison, so many family members were already lining up outside when the fire broke out.
Anxious relatives climbed on to the prison fence, shouting out inmates' names at the burning building. Some prisoners waved their arms and T-shirts through window bars.
"Rusio Victor, wave a white T-shirt Daddy," shouted seven-year-old Yadira Lopez, appealing to her father to signal he was alive.
For some, there was relief.Gonzalo Sepulveda wept after managing to contact his brother Cristian.
"I'll die if something happens to him," Mr Sepulveda said."Those aren't animals they have in there. They are human beings who have made mistakes."