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Some 200 Chile fans stormed into the centre around an hour ahead of kick-off, raising major concerns about security at the World Cup in Brazil.
The FFC wants to punish the team's supporters for their behaviour by banning them from travelling to matches at both home and abroad.
"We are now studying ways of punishing these people so they will have to watch [World Cup] games from Chile from now on," FFC president Sergio Jadue told reporters on Thursday.
"That also goes for local matches in Chile as well as matches with visiting national teams. We never want to see these images again."
Some 87 Chilean fans were arrested and had to leave Brazil within 72 hours or be deported, said FIFA's director of security Ralf Mutschke, who described the security breach as "embarrassing." At least one Chile fan was injured and taken outside in a wheelchair.
Jadue said the Chilean embassy in Brazil was currently dealing with the problem, while he believes FIFA could open up an investigation.
"We need to separate ordinary justice from sports justice. I don't know what ordinary justice in Brazil will do but our embassy is dealing with the legal issues," Jadue said.
"In terms of sports justice it could well be that FIFA will open disciplinary proceedings against Chile. Probably we need to defend ourselves. But we do not know yet what the charges could be."