The theme of the nine-day festival, which will feature more than 100 movies, is ecology. Films include "The Cove," a documentary that depicts an annual hunt of dolphins in Japan. Festival organizers added it at the last minute in part because of pressure from overseas.
While the movie has won more than a dozen awards worldwide, it is not among the 15 Japanese and foreign films competing for the festival's top prize of $50,000.
"The Cove" has provoked outrage over the dolphin hunt in the seaside town of Taiji in southwestern Japan, where 2,000 dolphins are killed every year, mostly for meat.
The film shows fishermen banging on poles to frighten the dolphins into a cove, where they are killed with spears. The cove is closed off by barbed wire, and the movie crew had to film most footage covertly.
Japanese police say the film's American director, Louie Psihoyo, and other members of his crew violated trespassing laws.
"The Cove" will be screened Wednesday. Advance tickets for the film were already sold out, festival spokeswoman Haruna Koike said.
Psihoyos has said he plans to attend the screening, even though he could be arrested for the alleged trespassing.
Weaver's "Avatar" will also be screened. It is the first major Hollywood 3-D release that's not animation. Directed by James Cameron, creator of "Titanic" and "The Terminator," the sci-fi epic centers on humans placed inside alien skins to survive on a distant world.
Weaver waved and blew kisses to fans at the opening ceremony.
The festival opened with "Oceans," a documentary on sea life.