Pinochet, 91, died Sunday, nearly a week after he suffered a heart attack.
Pinochet led a military coup against Chile's Socialist government in 1973, set up a pro-American, but repressive government and ruled with an iron fist until 1990.
More than 3,000 people were killed or disappeared and 28,000 were tortured during his rule. His death brought many opponents into the streets of Santiago to celebrate. But the mood turned sour when police clashed with demonstrators who threw rocks and erected barricades along the capital's main avenue. Tear gas and water cannons were used to disperse the protesters, many of them masked, who quickly regrouped.
The Chilean government called for calm in the wake of the clashes.
"The government makes an appeal to peace," Deputy Interior Minister Felipe Harboe said Monday morning. "We do not want people to be affected today by facts of the past."
The left-leaning government of Chile announced that there would be no official mourning and that the former dictator would be given a military, but not a full state, funeral. Chile's President Michelle Bachelet was one of many opposition leaders held and tortured by the Pinochet government during their brutal tenure.
Despite his record, several thousand supporters gathered outside the military hospital where Pinochet died and later lined up to see the former leader's body as it lay in a small chapel.
"He will live forever in my memory -- I love him as much as my own children," Margarita Sanchez told the Associated Press.
Pinochet's death also ended a decade-long effort to prosecute the former dictator for crimes committed by his regime.
He was placed under house arrest while in London for back surgery in 1998 after a Spanish court indicted him on 94 counts of torture and one count of conspiracy to commit torture.
The move sparked a 17-month legal argument over both the standing of Spanish authorities to try Pinochet for the crimes alleged and over the ailing dictator's mental and physical ability to defend himself.
Finally, in March 2000, Pinochet returned to Chile, but the legal fight followed him as Chilean courts and officials debated the possibility of a trial of the former strongman.
For some of those who sought his arrest and trial, Pinochet's death Sunday not only meant justice would be denied, but also demonstrated the shortcomings of international law.
"International justice tends to be slow, but I think that if we all make an effort we can do it (speed it up). It's absolutely necessary," said Baltasar Garzon, who issued the international warrant that led to Pinochet's arrest in London.
"To the end he was surrounded by lawyers trying to defend the indefensible," said Isabel Allende, daughter of the Socialist Chilean President Salvador Allende, who died in the 1973 coup.
"I would have preferred that the courts finished their work, I wish there had been a ruling, I wish he had been condemned," Allende told television in Spain, which she is visiting.