Russia fans have been at the centre of the troubles and tournament organisers UEFA imposed a suspended disqualification and a 150,000 euro ($168,300.00) fine on the Russian Football Union (RFU) on Tuesday.
The incidents have raised more questions about security at the World Cup in two years' time, adding to existing concerns about racism at Russian football matches.
"The policing and security infrastructure of major events of the scale of the Euro and the FIFA World Cup are very complex in nature," said FIFA in a statement to Reuters.
"For the 2018 FIFA World Cup, detailed security planning began by the local authorities from the moment the host country was chosen," it added.
"The relevant Russian authorities are putting in place a comprehensive security concept for next year’s Confederations Cup and the 2018 FIFA World Cup."
FIFA added that the security would incorporate "any lessons learnt from other events such as Euro 2016 and Rio 2016 (the Olympics Games) in order to try to avoid any repetition of such incidents."
The game's ruling body however, did not directly answer a question on whether it could guarantee the safety of visiting supporters from organised groups of Russian hooligans.
FIFA also said it could not comment on whether it would follow up on sanctions imposed against Russia by European soccer's governing body UEFA.
"The FIFA Disciplinary Committee takes decisions based on the specific circumstances of each case. Therefore, please understand that we cannot comment or speculate on potential future scenarios."
(Reporting by Brian Homewood; Editing by Ken Ferris)
