Officers were called to the Armley area of the city at around 11.40am after reports of a group of people waving around a sword in park.
Three men had been seen getting out of a 4x4 vehicle in Armley Ridge Road, brandishing a large knife.
The trio then left the scene in another vehicle.
A police spokesman said: "Armed officers were deployed to the area and enquiries led to a nearby address where three men were arrested on suspicion of possession of an offensive weapon and possession of cannabis with intent to supply.
"A quantity of cannabis and a machete were recovered and two vehicles were seized."
The men, aged 19, 21 and 22, were later released on police bail pending further enquiries.