Authorities deployed a heavy police presence and many shops closed as a precaution against possible damage.
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The demonstrations, which followed clashes last weekend in which protesters fought with police, looted shops and vandalised property, were violent in Turin, Rome and Bologna, with clashes between officers and demonstrators. They were largely peaceful in Milan.
Reuters witnesses did not observe any shops being looted or property vandalised.
After calls for further demonstrations circulated on social media this week, authorities made extensive security arrangements and deployed large numbers of police officers to prevent a repeat of last weekend's violence.
Earlier on Saturday, Italian police said they had detained a person allegedly linked to organising the "October 17 Movement" - last weekend's protests - and had taken them to police headquarters in Milan for questioning.