Six men were injured in the incident involving two groups of men in the Castlemilk area of Glasgow on Saturday evening.
A 23-year-old man remains in critical condition in hospital and a 25-year-old is in serious condition, while the other four have been discharged.
Police said they sustained various injuries consistent with a variety of weapons being used, and two of them have injuries consistent with a firearm being used.
They are treating the incident as attempted murders and serious assaults.
Officers were called to the scene at Ballantay Terrace at around 8pm on July 8.
Detective Chief Inspector Martin Fergus of Police Scotland’s Major Investigation Team (West) said: “I understand that local people in the area are very concerned about this level of violence taking place in broad daylight on their streets, and I’d like to reassure them that we are doing everything that we can to track down everyone involved in this incident.
“Many people would have seen what happened and we ask that they come forward and support us in our investigation.
“We will have extra patrols in the area for the foreseeable future and we would encourage the public to come forward and speak to these officers with any information they have or indeed any concerns they have.”
He later told the BBC: “We’re working on the hypothesis this may well just be a localised feud amongst families, we don’t know at this stage, this is what we’re attempting to piece together.
“What I can confirm is that two individuals, two males, received injuries consistent with gunshot wounds, one of which is critical and fighting for his life as I speak. The other male also received critical injuries, however it is not thought to be life-threatening at this time.
“Other males also involved in the disturbance have received a varying array of injuries, all believed to be serious.”
Police do not believe the incident is linked to any others in the Glasgow area over the last few months or any ongoing police investigations, and said there is nothing to suggest the incident was racially motivated.
Anyone with information is asked to contact officers at Helen Street Police Station on telephone number 101 quoting incident number 3874 of July 8.
Alternatively they can call Crimestoppers anonymously on 0800 555111.