Officer Carlos Manfredi says several people were detained for questioning after the shooting Saturday evening.
The shooting triggered a chaotic scene as dozens of people ran screaming as officers carrying handguns rushed to the scene.
Manfredi says a 64-year-old man who was caught in the crossfire got shot in the arm. He's hospitalised in stable condition.
Four shots were heard in a witness video posted online.
Manfredi says the argument had nothing to do with the gay pride event.
A concert that was part of the weekend-long gay pride celebration across the city was ending around the time of the shooting.
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News/World News/ One person wounded in shooting at San Francisco gay pride event