Fresh clashes also broke out in Tebourba, a town 40 km west of Tunis where one protester was killed on Monday, witnesses said, and soldiers could be seen there and in Jelma, a central town where clashes were also reported.
"Three hundred and thirty people involved in acts of sabotage and robbery were arrested last night", Reuters quoted Interior Ministry spokesman Khelifa Chibani as saying.
The protest movement began spontaneously after a few people tagged the phrase on walls across cities in Tunisia.
The Popular Front opposition group has called for a mass protest to be held in the capital Tunis on Sunday to mark the seventh anniversary of the Arab Spring uprising which toppled President Zine El-Abidine Ben Ali.
Tunisian Prime Minister Youssef Chahed warned against any attempt to disrupt the country, and against any vandalism targeting citizens, or public and private assets.
He says encouraging social unrest, violence and pillage by bringing young people out into the streets, who then get arrested, is not in anyone's interest. "People have to understand that Tunisia faces many challenges, but 2018 will be the last hard year for the Tunisians", he said.
"The violence has been amplified", he argues, "by some politicians calling for protests at night", rather than during the day, which is the usual custom in Tunisia. A video circulating on Facebook on Tuesday purportedly showed how police ran over the 55-year-old man, but the country's interior ministry denied the allegations and insisted he died from "chronic shortness of breath".
Clashes between demonstrators and security forces have taken place in at least 20 cities and towns, The Guardian reports.
Olfa Lamloum, the Tunisia country manager for International Alert, a nonprofit that seeks peaceful resolution to conflicts, said she anxious "that we have the same narrative as before the revolution".
"Stuck between the International Monetary Fund and a restive population, the government can not simply try to please both and will need to come up with a new economic policy and narrative to break out of this impasse", said Riccardo Fabiani, senior North Africa analyst with Eurasia Group in London.
Tunisians have started to express frustration over austerity measures expected to further increase prices in a struggling economy.