Tunisia's leaders started talks on Thursday with opposition and civil society representatives to try to defuse the country's latest political crisis, prompted by last week's murder of an opposition MP.
The talks come as supporters and critics of the government continue to hold street protests every night after breaking the Ramadan fast, particularly in Bardo Square outside parliament.
President Moncef Marzouki, a secular ally of the ruling Islamist Ennahda party, met leaders of the Republican Party, who are demanding "a national salvation government" led by an independent, a video released by the presidency showed.
Maya Jribi, a Republican leader, said "the rescue of Tunisia lies in the formation of a national salvation government headed by an independent and consensual personality whose members will not stand in the forthcoming elections, with a programme to combat terrorism and political violence."
Marzouki did not comment.
Mohamed Hamdi, member of the Democratic Alliance, called for "a government of skills" and a team of leading political figures to support it, particularly in drafting a new constitution.
Meanwhile, Islamist Prime Minister Ali Larayedh met Houcine Abassi, secretary general of the powerful UGTT union, which has called for the formation of a government of technocrats.
Neither made a statement about the meeting.
But Social Affairs Minister Khalil Zaouia said "the meeting was long, in order to evaluate the current situation and solutions for ending the crisis and for fighting terrorism."
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The secular Ettakatol party, Ennahda's coalition partner, has also demanded the government's departure.
Larayedh has refused to step down, promising a new constitution by August and elections in December.
But the proposed constitution does not enjoy consensus, and 60 deputies have demanded the dissolution of the transitional constituent assembly.
On Wednesday night, thousands of supporters and critics of the government held demonstrations.
Ennahda party has also called for a rally on Saturday night at the central Kasbah square to support "legitimacy and institutions and to denounce violence and terrorism."
The Thursday killing of Mohammed Brahmi, the second assassination of an opposition figure since February, has fuelled growing calls for the resignation of the coalition government headed by Ennahda.
Many Tunisians blame the government for the two killings, particularly for failing to rein in radical Islamists accused of a wave of attacks since strongman Zine El Abidine Ben Ali was toppled in a popular uprising in 2011.
Tension is mounting as Tunisia was in national mourning for eight soldiers slain by militants near the Algerian border.
On Wednesday, a roadside bomb went off as a national guard patrol passed south of Tunis early on Wednesday without causing any casualties or damage.
Ennahda is seeking to defuse the crisis by calling for a new national unity government that would include more parties.