The fighting broke out at around 4:55pm on Monday in the High Street, near to Portobello Police Station.
One local told the Evening News that the fight involved around 60 youths and that at least one of them was slashed in the face with bottles being thrown.
She said: “It was a group of around 60 kids between 13 and 18. Throwing bottles and fighting. One was slashed on the face. Not really a joking matter.
“In addition. The police station is only a part time station, so never open. Hence the police cars.”
Another eyewitness, Jacqueline Ramsay said: “Driving past, I could not believe no one came out of the police station.
“Cars honked horns to divert aggressive teenagers to disperse them. It seemed to help a bit.
“I hope whoever got hurt is okay. The whole lot of them should be arrested. There must be CCTV about.”
Police confirmed that two males aged 15 and 17 sustained facial injuries in the fighting.
Detective Sergeant Mark Lumsden from the Violence Reduction Unit said: “At this time, we do not know how many people have been part of this altercation, or what the reason for it was.
“As such, we are keen to hear from members of the public who were in the High Street area on Monday afternoon and witnessed what happened.
“In addition, anyone who can help us identify any suspects for this incident should also contact police immediately.”
Those with inormation can contact the VRU via 101 and quote incident number 3167 of the 25th June. Alternatively, an anonymous report can be made to the charity Crimestoppers on 0800 555 111.
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