Rome is counting the cost of its worst violence in years, which erupted on a day of global protests over austerity and banking practices.
The city's mayor says damage costing more than 1m euros (£877,000) was caused when hooded protesters torched cars and attacked banks and a church.
Mayor Gianni Alemanno described those responsible as "animals".
Saturday's protests affected 950 cities in 80 countries. They began in New York as "Occupy Wall Street" a month ago.
Italy's Ansa news agency said 135 people were injured including 105 police officers. Of the 30 protesters injured, two had fingers amputated due to exploding smoke bombs, officials were quoted as saying.
Scores of people are still being treated in hospital.
"We have to act with appropriate toughness against these animals," Mr Alemanno said as he visited the area around St John Lateran square near the city centre.
"There was a million (euros) in damages to public property and you have to factor in damage to private property too."
Interior Minister Roberto Maroni called for "exemplary" punishments for those responsible and said he would brief the Senate on Tuesday about the rioting.
About 20 people have been arrested and charged so far in connection with the violence. Mr Alemanno said he expected more arrests after police had studied video footage.
The BBC's David Willey in Rome says Italians are astonished how several hundred protesters - many dressed in black and wearing crash helmets - managed to cause mayhem in the capital.
Police said they had found unexploded petrol bombs in several streets.
Vatican spokesman Federico Lombardi said the 18th-Century church of Santi Marcellino and Pietro was "desecrated" by protesters.
Its parish priest said a statue of the Virgin Mary had been thrown into the street and smashed.
Rome resident Antonino Fiuggi told Reuters news agency: "These kind of things should not happen in a civilised country, these things should not be allowed."
Italian Prime Minister Silvio Berlusconi said those responsible for the violence "must be condemned by everyone without reservation".
Protests were continuing in a number of cities on Sunday.
In London about 250 protesters, who have erected about 70 tents outside St Paul's Cathedral, vowed to occupy the site indefinitely, mirroring the New York protest.
Protester Jane McIntyre told Reuters: "People are saying enough is enough, we want a real democracy, not one that is based on the interests of big business and the banking system."
Foreign Secretary William Hague told the BBC that protests would not solve the problem, but admitted he had some sympathy for those affected by "too many debts built up by states".
'We got sold out'
In New York overnight, police arrested about 70 people as the Occupy Wall Street protesters moved to Times Square.
Forty-five were detained in the square, with another 24 held for alleged trespassing at a branch of Citibank near Washington Square Park.
Organisers of the march from Zuccotti Park in Lower Manhattan to Times Square said about 5,000 people took part.
Protesters chanted: "We got sold out, banks got bailed out" and "All day, all week, occupy Wall Street."
One woman was injured when she fell as police on horseback tried to clear protesters from Times Square.
There were also protests in a number of other US cities, including 5,000 people who rallied outside City Hall in Los Angeles and 2,000 who marched in Pittsburgh.
In Saturday's other protests:
- A huge rally in Madrid had a festive atmosphere with tens of thousands filling the Puerta del Sol Square
- In Portugal, 20,000 marched in Lisbon and a similar number in Oporto
- In Greece, about 2,000 people rallied outside parliament in Athens and a similar number in the second city, Thessaloniki
- There were protests across Canada, including in Toronto, Halifax and Vancouver
- Thousands marched in Mexico, Peru and Chile
- Tokyo, Sydney and Hong Kong held protests