Sen. Isabel Allende, his daughter, read a statement on behalf of the family expressing confidence that the examination by international forensic experts would put any uncertainty to rest.
"Our conviction is that the president took the decision to die as a gesture of political coherence in defense of the mandate given him by the people," she said.
Other politicians from Allende's leftist coalition also attended the ceremony as the urn, wrapped in the Chilean flag, was removed from the cemetery.
The president's family has long accepted that he shot himself as his own air force bombed La Moneda, the presidential palace, Sept. 11, 1973, although some supporters still maintain he was assassinated.
Roberto Avila Toledo, an attorney who pressed for the exhumation, told La Tercera that even if is established that Allende died by his "own hands, it also gives rise to criminal liability. The death was caused by the coup. He was not a person possessed by a depression that would lead to ending his days."
Forensics chief Patricio Bustos said laboratory work on the remains would begin this week.