Street protests began before daybreak, with bonfires and violent clashes with police. One station was attacked in suburban Santiago and hooded activists occupied a major avenue, resulting in 10 arrests.
A memorial ceremony for Allende on Sunday also ended in violence after human rights activists spoke of the unresolved legacies of a military regime that killed more than 3,000 people.
Interior Minister Rodrigo Hinzpeter called for calm, saying that "the people suffering from this violence have nothing to do with what happened on Sept. 11, 1973."
Also Tuesday, Chile's Supreme Court closed the book on a judicial review of Allende's death, confirming the conclusion of a lower court last December that the socialist leader committed suicide.
The lower court said Allende fired an assault rifle that he held under his chin as Pinochet's troops closed in during a ferocious aerial bombardment of the presidential palace.
Four decades later the death remains an open wound for many Chileans.
When leftist lawmakers held a moment of silence Tuesday, right-wing legislator Ignacio Urrutia publicly disagreed with the gesture, asking his fellow lawmakers why they would honor "a coward who committed suicide." The outburst was widely condemned by Chileans on social networks.