Bilbao mayor Juan Mari Aburto has condemned the violent incidents before and during Athletic Bilbao's game against Marseille -- one of two Europa League contests marred on Thursday by clashes between supporters.
Three Marseille fans were detained by police and two security guards were taken to hospital, one after being stabbed in the neck by a sharp object.
Meanwhile, at least eight police officers were injured in scuffles with home fans before Lyon's game against CSKA Moscow in France.
Those incidents occurred nearly a month after a Bilbao police officer died of cardiac arrest before Athletic's Europa League game against Spartak Moscow.
"Deplorable attitude by some 'fans' of Marseille," Aburto wrote on Twitter. "I reiterate my revulsion over these undesirable ones that hide in football to bring out their true violent, ultra and unsportsmanlike face. I wish a prompt recovery to the two Athletic security guards."
El Correo reported that officers confiscated knives, metal bars, golf balls and flares from a section of Marseille fans prior to the game.
The game, which Marseille won to advance to the quarterfinals on aggregate, was considered "high risk" by local authorities. A total of 800 officers, including 200 from a private security firm hired by Athletic, were placed on duty.
However, Marseille supporters still managed to take flares into the stadium, light them and throw them towards the home fans during the game.
In Lyon, two riot police officers were seriously injured and six others sustained minor injuries before the game as a group of Lyon ultras clashed with officers outside the Groupama Stadium.
Three arrests were made, RMC reported, after at least 100 people attacked a specialised police unit, hurling missiles and seriously damaging their vehicle before riot police arrived to break up the group.
The first leg of Lyon's Europa League quarterfinal against Besiktas last April was marred by violence that led to €100,000 fines for each club and a two-year suspended ban from European competition that would activate in case of further incidents.
It is not clear if any of the 400 CSKA fans, who saw their team triumph 3-2 to go through to the quarterfinals, or the estimated 100 Spartak supporters who had accompanied them were involved in the violence.
ESPN FC's France correspondent Ian Holyman contributed to this report.