About 50 policemen were wounded in that violence and 237 people were arrested, including two Islamists, said interior ministry spokesman Khelifa Chibani.
Tunisia deployed more than 2,000 troops countrywide to protect "sovereign institutions", Defense Ministry spokesman said.
This security forces' behavior is a key factor in Tunisia's success in preventing the demonstrations from degenerating into violent protest.
Some protesters told Xinhua that the new law has led to the price increase in some consumer products, as it doesn't meet the expectations of the middle class, but harms the purchasing capacity of the Tunisians.
The main opposition party had hours earlier called for protests to continue until the government scrapped what it called an unjust 2018 budget including price and tax hikes.
Unrest is also reported in the cities of Gafsa, Kazierin and Sidi Bouzid, where the protests that marked the beginning of the Arab Spring began in 2011.
On Tuesday, petrol bombs were thrown at a Jewish school on the southern tourist island of Djerba, home to an ancient Jewish community.
The protest had turned violent when security forces tried stopping some youths from burning down a government building, witnesses told the media.
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Opposition forces have called for halting the implementation of the 2018 budget and rolling back on austerity measures by the government and vowed to escalate the rallies in the coming days. He said people who were arrested had taken part in theft, looting and arson.
Last year, the Washington-based International Monetary Fund agreed a four-year loan programme worth about $2.8 billion with Tunisia, tied to economic reforms.
Tunisians have already been struggling with high unemployment and rising prices.
"We're concerned about the high number of arrests, some 778 people we understand have now been arrested since Monday, and around a third of those arrested were between the ages of 15 and 20 so very young", United Nations human rights spokesman Rupert Colville told reporters in Geneva.
The demonstrations have so far been much smaller than previous protests since the overthrow of autocrat ruler Zine El-Abidine Ben Ali in 2011.
Hammami said the government's austerity measures were to blame for the economic situation.
The 2011 Arab Spring uprising and two Islamist attacks in 2015 have stymied foreign investment and tourism, which accounts for eight percent of Tunisia's economy.