Before voting 8-3 for the measure, supervisors rejected a competing resolution to welcome the torch of the 2008 Beijing Games "in the true spirit of the Olympics," The Los Angeles Times reported Wednesday.
Advocates for Tibet, Darfur and the religious sect Falun Gong are among groups that plan to protest the April 9 arrival of the torch in San Francisco, a city that is a third Chinese-American.
Protesters are promising to line the streets along the six-mile relay route with banners and placards opposing what they charge are China's repressive policies.
"People have the right to protest, but they don't have the right to deny the torch to come here," Mayor Gavin Newsome said. "They are losing sight of what the Olympics are all about."
The mayor criticized the supervisors' action Tuesday.
"This is par for the course in San Francisco. You could have written this script beforehand," he said.