The fight reportedly broke out at a party at a school hall in Calbourne Avenue around 9pm on Saturday (March 22).
Video footage appears to show knives being wielded among a large group of young people, sending them running and screaming onto the street.
Police confirmed two boys, 16 and 19, were stabbed and taken to hospital with injuries thought not to be life-changing.
Margaret Mullane, MP for Dagenham and Rainham, said: “I was shocked and utterly condemn, the appalling disorder which took place in Elm Park over the weekend.”
Police who were called to reports of a “number of teenagers” fighting were met with aggression and officers were treated for injuries.
Three teenagers were arrested at the scene on suspicion of assaulting emergency workers and taken to an east London police station before being bailed.
Mullane added: “I am led to believe none of the injuries were life changing or life threatening, which is a relief for the parents of the victims, and for the police who also suffered injury.
“In the coming days I will be liaising with the Metropolitan police, to ascertain how so many youths were able to carry out an attack like this.
“I will be asking why dispersal was the route taken by officers.”
Havering Daily has reported that the incident happened at a 16th birthday party at Elm Park Primary School hall.
It adds that around 50 youths were involved in the incident, and knives were left discarded in front of resident’s driveways – although this has not been verified by the police.
Anyone with information relating to the incident is asked to call 101 or message @MetCC on X giving the reference 6940/March.