Kick-off for the first leg of the quarter-final in France was delayed by around 45 minutes after ugly scenes and clashes between fans on Thursday.
Sabah, another pro-government daily website, claimed: "Lyon hooligans attacked the Turkish fans, including women and children and afterwards the Besiktas fans responded".
"Projectiles and fireworks launched from the stands require fans to take refuge on the pitch", Lyon tweeted.
Crowd disorder inside the stadium has delayed the kickoff in the Lyon-Besiktas Europa League quarterfinal first-leg game.
"Disciplinary proceedings have been opened following the UEFA Europa League quarter-final match between Olympique Lyonnais and Beşiktaş JK (2-1), played on 13 April in France", the statement read.
Fans were snapped angrily clashing with armoured police, most wearing black signalling the club's Ultras - and some waving the Turkish flag and letting off smoke bombs.
There was also violence outside the Parc Olympique Lyonnais stadium before the game, which Lyon won 2-1 with a late victor.
UEFA has increased security since an explosion rocked the Borussia Dortmund team bus on Tuesday as it was transporting players to the Champions League tie with Monaco.
The trouble was concentrated in a section behind one goal housing Besiktas fans, and followed clashes between rival groups on the streets.
The return match is next Thursday in Istanbul which has a reputation as among the most hostile cities in Europe for visiting fans. "It would be very unsafe to take on this team (in presence of) the same supporters as tonight".
A violent altercation broke out in the stands minutes before a major European soccer match was set to begin.
Stewards looked to be injured from the violence as police and medics tried to safely take them away from the violence.