At least one person is reported to have been killed and a large area of the city centre has been closed off by police and the military.
It comes after violent scenes in the capital overnight despite a night-time curfew being put in place.
At least 23 people have died since nationwide protests over poverty and corruption began last month.
President Zine al-Abidine Ben Ali has called the unrest a "terrorist act".
The BBC's Adam Mynott in Tunis says the unrest has now reached the central streets of the capital, close to shops, banks and the French embassy.
Police have put up road blocks and have fired tear gas to push back crowds gathering to watch the events, our correspondent adds. There have been reports of looting.
Witnesses said at least one person had been shot and another seriously wounded.
It comes after one protester was reportedly shot dead in a western suburb of Tunis, and three others in a southern area of greater Tunis. Rights groups said up to eight people had died.
France, the former colonial power in Tunisia, has called on the government to show restraint while the US has warned its citizens to defer non-essential travel to the country, citing "intensifying political and social unrest".
The protests reached the capital for the first time on Wednesday afternoon, as protesters threw stones and police responded with volleys of tear gas.
An indefinite night-time curfew was put in place but overnight, youths fought battles with security forces and set fire to buildings.
More clashes were reported from at least half a dozen towns across the country, including Sfax, Douz and Thala.
Reuters reported up to 10,000 people were on the streets in Sidi Bouzid.
"It is not just about unemployment any more," one protester said. "It's about freedom of expression, freedom of assembly, all the freedoms."
Switzerland's foreign ministry has confirmed that a woman who had dual Swiss-Tunisian nationality was killed in the north of Tunisia.
Swiss Radio said she was hit in the throat by a stray bullet while watching a protest late on Wednesday in the town of Dar Chaabane.
A foreign ministry statement said the Tunisian ambassador had been summoned, and called on the Tunisian government to "respect dialogue, fundamental liberties and human rights", including freedom of assembly.
French diplomats have also reportedly informed the family of a French-Tunisian academic, Hatem Bettahar, that he was one of two protesters killed by the police on Wednesday in the central town of Douz.
Mr Bettahar, a computer science lecturer in France, had been visiting his mother. A Tunisian teacher has said he has posted on the internet a video showing Mr Bettahar lying in a pool of blood after being shot.
French Prime Minister Francois Fillon has criticised the "disproportionate use of violence" and called on all sides to show restraint.
The reaction article is also worth reading, especially the commentary from the Tunisian human-rights lawyer at the bottom.
Things appear to have calmed down greatly in Algeria for now (according to news sources and people I know there), but Tunisia -- long perceived to be stable and comfortable and friendly to Western interests -- appears to be in the midst of something large-scale.
I know this is on the heels of another Tunisia post -- about France's reluctance to criticize -- but given that EU citizens are being killed, and Tunisia's economy is based a lot in tourism, particularly European tourism, this might inspire less fence-sitting.
Mods, no Tunisia tag.