Tunisian political leaders have started efforts to fill the power vacuum created by the fall of President Zine al-Abidine Ben Ali amid mass protests.
Interim leader Foued Mebazaa - who was sworn in on Saturday - promised to form a unity government.
The country appears to be mostly quiet, although gunfire was heard in Tunis during a second overnight curfew.
The previous night had seen widespread violence, including looting, torching of buildings and deadly jail riots.
Two people were reported to have been shot dead by soldiers near the interior ministry on Saturday.
Some of the violence is being blamed on supporters of former President Ben Ali, who fled to Saudi Arabia on Friday.
Election demand
The BBC's Adam Mynott in Tunis says the immediate future of the country, thrown into unprecedented turmoil, is in the hands of the military.
Mr Mebazaa, who until Saturday was the Speaker of parliament, has asked Prime Minister Mohammed Ghannouchi to form a national unity government.
"All Tunisians without exception and exclusion must be associated in the political process," Mr Mebazaa said in a televised address.
Opposition leader Najib Chebbi told France's RTL radio that he had already held talks with Mr Ghannouchi about taking part.
He said his main demand was that elections should be held "within six or seven months" under international supervision.
Under the present Tunisian constitution a presidential election must be held within 60 days.
Another opposition figure, Mustafa Ben Jaafar, told Reuters news agency that he too had been contacted and called for "real reforms".
Further talks are expected on Sunday.
The exiled head of Tunisia's Islamist party, Rached Ghannouchi, said he would return to the country within weeks.
Speaking to the BBC in London, said Tunisians had got rid of a dictator, but they had a long way to go were a long way from bringing down the dictatorship.
Gaddafi wades in
The centre of Tunis has been sealed off by tanks and troops guarding key public buildings. Army helicopters are patrolling overhead.
Residents in some areas have armed themselves with sticks and clubs, forming impromptu militias to protect their homes.
Many attacks appeared to target businesses and buildings connected with the former president and his family.
French-owned supermarkets were also looted and the main railway station in Tunis was badly damaged by fire.
Saturday's deadliest incident appears to have been in the resort of Monastir, about 160km (100 miles) south of Tunis, where fire swept though a prison, killing at least 42 people.
Inmates are believed to have been attempting to escape, as they did at a number of other jails where violence was reported.
The leader of neighbouring Libya, Muammar Gaddafi, became the first Arab leader to speak out about the fall of the Tunisian president. He said the ensuing violence was "not worth it.
"You have suffered a great loss... There is none better than Zine (Mr Ben Ali) to govern Tunisia," he said in a speech broadcast on state television.
He added that he still considered Mr Ben Ali to be the "legal president of Tunisia".
In the past month, protests have swept the country over unemployment, food price rises and corruption. Security forces used live ammunition against protesters and dozens of people died.
Mr Ben Ali, who had been in power for 23 years, was only Tunisia's second president since independence in 1956. He conceded power on Friday after the unrest culminated in a giant rally against him in Tunis.
