Tunisian forces are exchanging fire near the presidential palace with members of deposed President Zine al-Abidine Ben Ali's guard, reports say.
Witnesses reported heavy gunfire in Carthage, north of the capital Tunis, where the palace is located.
It comes after the ex-head of presidential security, Ali Seriati, was arrested and accused of threatening state security by fomenting violence.
Meanwhile, political leaders are holding talks about a new government.
Interim leader Foued Mebazaa, who until Saturday was the speaker of parliament, has asked Prime Minister Mohammed Ghannouchi to form a government of national unity.
In a national TV address, Mr Ghannouchi said an agreement between the political parties would be announced on Monday. He also pledged "zero tolerance" against anyone threatening the security of the country.
The announcement of Mr Seriati's arrest on Sunday came after the previous day saw widespread violence across Tunisia, including looting, arson and deadly jail riots.
The BBC's Wyre Davies, in Tunis, says that while the Tunisian army does not appear to be interfering in the process of political reform, the motives of some members of the police and security services loyal to the ousted president may be more sinister.
Hours after Mr Seriati's arrest was announced, heavy gunfire erupted near the presidential palace in the Carthage area.
"The army has launched an assault on the palace... where elements of the presidential guard have taken refuge," AFP news agency quoted a Tunisian military source as saying.
An eyewitness quoted by Reuters news agency said: "There is firing from around the presidential palace, intensive and continuous."
There was also gunfire near the interior ministry and the headquarters of an opposition party. Two gunmen firing from a roof near the interior ministry were reportedly shot dead by the security forces.
In another development, a group of Swedish nationals - who were apparently in the country on a wild boar hunting trip - were attacked and badly beaten in Tunis amid reports that foreign nationals were among the presidential guard.
There have also been attacks targeting businesses and buildings connected with the former president and his family.
Residents in some areas have armed themselves with sticks and clubs, forming impromptu militias to protect their homes from looters.
Before the upsurge in violence on Sunday, the interim government had shortened the overnight curfew by four hours.
Curfew hours - which ran from 1700 (1600 GMT) to 0700 (0600 GMT) for two nights - are now between 1800 and 0500.
A state of emergency remains in force and there is very little economic activity. Schools, government offices and most shops are closed.
The US Secretary of State, Hillary Clinton, has urged Tunisia's new leadership to restore order and adopt broad economic and political reforms.
Mr Ben Ali, who had been in power for 23 years, fled to Saudi Arabia on Friday after a month of mounting protests across the country over unemployment, food price rises and corruption. Dozens of people were killed during this period as police opened fired on demonstrators.
Under the present Tunisian constitution, a presidential election must be held within 60 days.