Three people were arrested after an altercation amongst fans following Friday night's match between Dundalk and Drogheda United at Oriel Park.
Dundalk won the match 4-2 to move five points clear of Louth derby rivals Drogheda who remain rooted to the bottom of the SSE Airtricity Men's Premier Division.
But the fixture was marred by post-match clashes on the pitch between supporters.
Gardaí confirmed to RTÉ Sport that three arrests have since been made, two of which were dealt with under the Garda Juvenile Liaison Scheme, while one man was dealt with by way of an adult caution.
In a statement, Drogheda United described the post-match scenes as "unacceptable" and "unsavoury", and indicated that they will decide on "appropriate sanctions" after a review of all footage and facts.
"All involved in Drogheda United sincerely apologise, especially to the families, but to all who witnessed the post-match altercations in Dundalk last night," the club said.
"The events that occurred after the match were unacceptable, and as a club, we condemn this unsavoury and violent behaviour.
"We are working closely with security staff, photographers and tv crews to identify the individuals involved and will determine appropriate sanctions once we have reviewed all the footage and have all the facts.
"Rest assured there is no place for this behaviour in our club. The vast majority of our fans are exceptional, unfortunately we have been tainted by a very small minority.
"We will continue to focus on building and bettering a safe sporting environment for all to enjoy."
Dundalk also issued a response, which read: "Dundalk FC strongly condemns the disgraceful scenes that took place at the end of Friday night's SSE Airtricity Men’s Premier Division fixture with Drogheda United at Oriel Park.
"We are working closely with the FAI, Drogheda United and the Gardai to review the incident and will issue a further update in the coming days. Finally, we would like to thank our supporters for their cooperation and patience while members of our security team and the Gardai dealt with the matter."
A League of Ireland statement said that it "condemns in the strongest possible terms the incidents involving supporters following the conclusion of last night's fixture between Dundalk and Drogheda United.
"We are working closely with An Garda Síochána, Drogheda United and Dundalk while reviewing the Match Delegate’s report on the fixture and will communicate any further information relating to disciplinary action following the conclusion of this process."
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