Police were called at around 1.45pm on Monday, August 24, to an incident involving several people on Calenick Street.
One man suffered a “potentially serious injury”, while two others sustained minor injuries.
Armed officers attended the scene, and a guard was put in place.
Two men in their 20s were arrested on suspicion of causing grievous bodily harm with intent and remain in police custody.
Police say those involved are believed to be known to each other and that there is “no wider threat to the public.”
A video posted online allegedly showed a brawl involving several men brawling on the street, including a shirtless man carrying a large blade.
A spokesperson for Devon and Cornwall Police said: “We are appealing for witnesses and footage following a large fight in Truro.
“Those involved are believed to be known to each other and there is no wider threat to the public.
“We are aware of footage circulating on social media.
“Anybody who witnessed the incident or who has relevant footage who has not yet contacted police is asked to get in touch via 101 or our website quoting 50260226230”
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