Officials raided "known anarchist circles all across the country, from Trentino to Lombardy, from Lazio to Sicily," ANSA reported.
"They were looking to kill someone," Interior Minister Roberto Maroni said.
Six people were arrested in Florence and 12 people were arrested in Rome, police confirmed.
During Saturday's Day of Rage in Rome, police said demonstrators attacked property, police and vehicles during a march against corporate greed and economic equality. Witnesses said the peaceful marches were hijacked by violent radicals.
Police said about 200,000 protesters traveled to the capital from across Italy. The number of radicals ranged from "scores" to up to 800, ANSA reported.
Maroni said "no stone would be left unturned" to identify and find those who had turned Rome into "a battlefield," and called for "exemplary punishments" for those responsible.
Some on the far left said some of the anarchists were plants working with the police to discredit the peaceful demonstrators, ANSA said. The claim was dismissed by members of Parliament who said the violence was "of a clear origin."