Police are appealing for information as well as condemning the disorder seen in The Meadows this weekend.
A 17-year-old youth suffered serious injuries during the disturbance and a 22-year-old man was attacked during the disturbances.
So far three people have been charged in connection with anti-social behaviour and a serious assault.
Officers will continue to provide a presence in The Meadows over Easter and the coming weekend and will not hesitate to use their enforcement powers as a last resort.
Chief Inspector Sarah Taylor of Edinburgh Police Division said: “We are aware of the extent of the disorder seen in The Meadows this weekend and we absolutely condemn this.
“Officers were called to a number of incidents over the course of the day and responded quickly and professionally in the face of some blatant anti-social behaviour.
“Hundreds of people were moved on or dispersed from the area.
“Three people have so far been charged in connection with anti-social behaviour and a serious assault, and we are working to trace others involved in various incidents.
“In particular, we’re eager for anyone who saw a 22-year-old man being attacked around 7.30pm in the Middle Meadow Walk area and also a 17-year-old man being seriously injured in the park around 6.40pm, to come forward.
“Anyone who witnessed these incidents, who has seen information online or has footage which may be relevant is asked to contact Police Scotland on 101, quoting incident 1635 of 3 April, 2021. Information can also be passed anonymously to the independent charity Crimestoppers on 0800 555 111.
“Be assured that there will be a continued police presence at The Meadows over Easter and the coming weekends, as a minimum. We’ve been working with the council and are committed to tackling these issues together, both in the immediate future and long-term. There will be zero tolerance.”
Officers are also urging people to do the right thing to prevent the spread of coronavirus.
CI Taylor continued: “We’ve urged people to stay local and follow the regulations on gatherings. Saturday saw several thousand people congregate at The Meadows and, disappointingly, some were intent on disorder.
“The coronavirus regulations have had a significant impact on our lives and I would like to thank those who are sticking to the rules and doing the right thing to avoid the spread of the virus as we move through the easing of restrictions.
“Our approach throughout the pandemic has been to engage with the public, explain the legislation and encourage compliance, but we will not hesitate to use our enforcement powers as a last resort.”