One of the five people arrested at Wednesday's Edinburgh derby was identified to police by other fans, Hearts owner Ann Budge has revealed.
Hibs boss Neil Lennon was struck by a coin at Tynecastle, Hearts goalkeeper Zdenek Zlamal claims he was punched by a fan, while both assistant referees were also targeted.
In a joint statement, Hearts and Hibs condemned the "unsavoury" incidents.
The clubs say the culprits will "face appropriate sanctions".
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A 25-year-old man has been charged with assault after an assistant referee was attacked, while Police Scotland have confirmed investigations continue into incidents involving Lennon and Zlamal.
Hibs chief executive Leeann Dempster said the "clubs are united" and called on fans to help identify those responsible "for this kind of unacceptable and potentially dangerous behaviour".
Budge said Hearts will work with their city rivals and Police Scotland to identify those responsible and "ensure they are banned from attending our two stadiums and are formally charged".
In the statement, she added: "By working together in this manner, we will succeed in removing the tiny percentage of fans, whose behaviour spoils things for the majority."
Budge also said that the clubs must not "fall into the trap of condemning the thousands of genuine football fans who do nothing more than passionately support their respective teams".
And Dempster said they will "learn any lessons that we can" and would "not allow the mindless actions of a few foolish individuals to jeopardise" the enjoyment and safety of other fans.
Scottish FA chief executive Ian Maxwell said he was sure "no stone will be left unturned" by the clubs and confirmed that both assistant referees were struck by missiles at Tynecastle.
"We cannot accept that two assistant referees simply carrying out their duties are put in that position," he added.
"I would like to commend their commitment and professionalism in seeing the game through to its conclusion."