FIFA has opened disciplinary proceedings looking into the clashes at Wembley Stadium between police and Hungarian supporters at Tuesday's game against England, saying it has "zero tolerance against such abhorrent behaviour".
World football's governing body added on Wednesday that it has also started investigating incidents during the game between Albania and Poland in Tirana, where bottles were thrown on the pitch after Poland scored.
"Following an analysis of the match reports, FIFA has opened disciplinary proceedings in relation to yesterday's England v Hungary and Albania v Poland FIFA World Cup qualifier matches," FIFA said in a statement.
"Once again, FIFA strongly condemns the incidents at both matches and would like to state that its position remains firm and resolute in rejecting any form of violence as well as any form of discrimination or abuse.
"FIFA has a very clear zero-tolerance stance against such abhorrent behaviour in football."
Police came under attack from Hungary fans at Wembley after they moved into the "away section" and had to retreat.
The Metropolitan Police said they had taken action after a steward was racially abused.
"Shortly after the start of tonight's match at Wembley, officers entered the stand to arrest a spectator for a racially aggravated public order offence following comments made towards a steward," the police said on Twitter.
"As the officers made the arrest, minor disorder broke out involving other spectators. Order was quickly restored and there have been no further incidents at this stage."