A firefight broke out late Sunday between the army and the bodyguards of former president Zine el-Abidine ben Ali near the presidential palace, witnesses told the German Press Agency dpa.
Prior to that the security situation had reportedly improved, with the state of emergency declared Friday being relaxed to an overnight curfew.
Tanks were still being deployed on the main avenue in Tunis and army helicopters flew over the city as the administration of interim President Foued Mabazaa sought to stamp out the lawlessness that took hold after longtime leader Zine el-Abidine ben Ali abruptly quit power Friday.
An interim government was expected to be named Monday. The temporary government will not include members of the previous ruling party, but will be made up of members of three opposition parties and independent authorities, Progressive Democratic Party leader Maya Jeribi said after a meeting among political leaders Sunday.
Ben Ali fled the country after a month-long uprising, which claimed at least 66 lives, according to one human rights group's count - mostly unarmed protestors shot by police.
Widespread looting and attacks on businesses and buildings associated with him and his regime followed his flight into exile in Saudi Arabia. Hundreds of tourists - mainly French - stranded in seaside resorts were still being evacuated on Sunday.
There were reports of Europeans being arrested, including a German couple reportedly armed with hunting rifles. The German embassy in Tunis however could not confirm the arrests. There were conflicting reports as to the nationality and number of those arrested.
The army and police accuse Ben Ali's presidential guard of deliberately stoking the unrest, saying members of his guard are driving around in rented cars, looting and shooting in the air to sow panic.
The head of the presidential guard Ali Soriati was arrested on Sunday.
In many areas, residents have organized themselves into neighbourhood militias to prevent attacks on cars, home and businesses.
Late Saturday saw continued unrest and shootings in parts of Tunis, which claimed the life of at least one person - a 30-year-old man shot dead by police in El Khadra suburb, according to residents speaking to the German Press Agency dpa.
A German-Tunisian national told dpa that as he was on his way to Tunis airport, "we were stopped five times by soldiers." The man's wife added: "I was totally frightened."
Meanwhile, the state of emergency was starting to affect food supplies in Tunis.
"We haven't had bread for three days," an elderly woman who was standing in a long queue for bread at the central market told dpa. Vendors at the city's main market complained that supplies hadn't been able to get through.
After being sworn in Saturday interim president Foued Mabazaa, the former parliament speaker, tasked Prime Minister Mohamed Ghannouchi Saturday, with establishing a transitional government of national unity.
A day earlier Ghannouchi had declared he would be the one to preside over the transition, but the constitutional council stepped in and declared Mabazaa the rightful interim leader.
The opposition, which was neutered under Ben Ali's rule, has been demanding to play a part in the new order, saying the current administration is corrupt and tainted by the police killings of demonstrators.
US Secretary of State Hillary Rodham Clinton on Sunday urged Tunisia to restore order "in a responsible manner as quickly as possible" during a telephone call with her Tunisian counterpart Kamel Morjane.
She also "underscored the importance of addressing popular concerns about the lack of civil liberties and economic opportunities, and the need to move forward with credible democratic elections," according to a statement from her office.
But the United States had been encouraged by the "willingness" shown by interim president Foued Mabazaa and Prime Minister Mohamed Ghannouchi to work with "Tunisians across the political spectrum," she reportedly told Morjane.
Tunisia's turmoil began in mid-December when a young unemployed man burned himself to death to protest the authorities' indifference to his plight.
That act triggered widespread demonstrations over unemployment and corruption, which swelled into a full-scale uprising.