IOC and Rio organizing committee leaders attended Thursday's flame-lighting at Ancient Olympia, where antiquity's greatest sporting event was held for over 1,000 years.
They voiced confidence Brazil will overcome its political and economic problems to stage successful games, the first in South America.
The flame was lit by an actress impersonating a pagan high priestess and will be delivered to the first torchbearer, Greek world gymnastics champion Eleftherios Petrounias. It will traverse Greece for six days, until the April 27 handover to Brazilian officials in Athens.
After a brief stopover in Switzerland, the flame will start its travels through Brazil on May 3.