"The time has come not to forget, but to overcome the traumas of the past," Sebastian Pinera said in an address from the La Moneda presidential palace.
"The best legacy we can leave our children is a country reconciled and at peace," he said as he led a ceremony honoring the victims of the September 11, 1973 overthrow of then-president Salvador Allende.
In a sign of the persistent divisions in the South American country, disturbances broke out overnight in the capital Santiago.
In one neighborhood, attempts to set fire to a public bus filled with passengers was thwarted by the driver.
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Authorities played down the unrest, saying it was not unexpected. Clashes between protesters and police occur every year.
Police chief Gustavo Gonzalez Jure described the incidents as "relatively minor."
Pinera, Chile's first right-wing head of state since democracy was restored in 1990, stressed that reconciliation will require Chileans "to continue on the path of truth and justice."
He condemned those responsible for human rights violations during the 17-year Pinochet regime while singling out those of influence "who could have done more" at the time to stop the abuse.
Pinochet died in 2006 without ever having gone on trial and the Chilean court system has some 1,300 cases open involving crimes committed during his rule.