A group of Italy fans made fascist salutes and threw bottles at Bulgaria supporters before Saturday's World Cup qualifying Group Eight match in Sofia. Three supporters were also arrested for burning a Bulgarian flag.
"We will not ask for any more tickets for Italy matches abroad," Giancarlo Abete told Radio Anch'io.
The hard line, which must be agreed with the government, follows several years of crowd trouble within Italy which has led to heavy restrictions on away travel for league matches.
Italy partly missed out on holding the Euro 2012 championship because of their hooligan problem but Abete said not every fan was culpable.
Security is being stepped up for Wednesday's home qualification game with Montenegro in Lecce.
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