Officers investigating "terrifying" violence have arrested three people, including a 14-year-old boyOne man was reported to be carrying a large blade during disorder outside Asda on Newtown Road in Nuneaton at about 17:00 BST on Friday.
An 18-year-old man from Bedworth was arrested in the early hours of Sunday on suspicion of violent disorder.
The 14-year-old from Coventry and a man, 18, from Bulkington, arrested on Saturday, have been released on bail.
Det Sgt Emma Mackay from Warwickshire Police said: "This was a terrifying incident in broad daylight that left members of the public shocked."
The force said extra officers had been in the area over the weekend to help prevent any further trouble.
It has released images of five people officers would like to speak to in relation to the incident.


Det Ch Insp Dave Andrews said the level of disorder in the town over the past week had been "totally unacceptable" adding the force understood the level of concern amongst local people.
Earlier in the week two 15-year-old boys were arrested after teenage girls were threatened with blades in a spate of linked robberies.
They have been bailed until next month pending further inquiries.