The demonstrations have hit neighbourhoods of the capital, Tunis, and several other towns.
Unrest is spreading throughout the country, including the central city of Kasserine and the northern towns of Siliana, Tebourba and Thala.
Civil society organisations have called for peaceful demonstrations against the new annual budget, which includes a steep rise in value-added tax but some of the protests have escalated into clashes with police.
The latest confrontation Wednesday night saw a provincial police station torched and Molotov cocktails hurled at security forces, who in turn used batons and teargas.
The budget law sparked the protests but they are fuelled by wider discontent, Mohamed al Marouani, a Tunisian economist teaching at Paris Sorbonne university, says.
Most citizens feel that their economic conditions haven't improve since the 2011 revolution that led to former strongman Ben Ali's eviction from power, he points out.
Even though there is now a democratically elected government, many economic indicators have actually worsened - unemployement has risen from about 13 percent to more than 15 percent, income from tourism has significantly dropped and the country's debt has soared from 40 percent to 70 percent, which explains why the authorities are trying to generate more tax revenue, Al Marouani explains.
Civil society organisations share this analysis.
The Tunisian Forum for Economic and Social Rights points out that the number of demonstrations has risen from about 5,000 in 2015 to some 10,000 last year.
Yet, so far, the authorities have failed to satisfy to public frustration and anxiety.
The initial response from Prime Minister Youssef Chahed was to condemn "acts of vandalism".
On Thursday he qualified that position by making a distinction between looters "who don't serve Tunisia's interest" and protesters.
"These young protesters live in harsh conditions," he told RFI's sister radio MCD. "They do not trust politicans any more but still have hope for their country and when they protest they do so peacefully. I want to assure them that any measures we take are aimed at bettering the life conditions of all Tunisians citizens."
The government should not focus on the few who take advantage of the unrest to vandalise and loot, but rather hear the majority's appeal to better their living conditions, according to Tunisian Forum president Messaoud Romdhani.
"When people grew frustrated at the time of Ben Ali, there was the alternative to seek more democratisation," Romdhani explains. "But now that we have an elected government, if it ignores the seriousness of the socioeconomic crisis, it could lead to new instability that can either fuel nostalgia for the previous regime, or worse, create a chaos that terrorists could try to benefit from."
Tunisia will never be taken over by terrorist groups, he believes. "But it remains a potent fear."