The offices of the moderate Islamist Ennahda party – which rules in a fractious coalition with secularists – was set ablaze after Chokri Belaid, 48, was gunned down outside his home in the capital, Tunis.
Secular parties have threatened to quit the assembly and have called a general strike for today when Mr Belaid will be buried.
Ennahda denied any involvement in the killing. Its leader, Rached Ghannouchi, said: "Is it possible the ruling party could carry out this assassination when it would disrupt investment and tourism? Tunisia is in the biggest political stalemate since the revolution. We should be quiet and not fall into a spiral of violence. We need unity more than ever."
Prime Minister Hamadi Jebali, a member of Ennahda, has condemned the killing as a political assassination and a strike against the Arab Spring revolution. He said: "Someone wanted to silence Mr Belaid's voice."
As Mr Belaid's body was taken by ambulance through Tunis from the hospital where he died, police fired teargas towards 20,000 protesters chanting for the fall of the government outside at the interior ministry.
Despite calls for calm from President Moncef Marzouki, who is not an Islamist, thousands also demonstrated in cities including Mahdia, Sousse, Monastir and Sidi Bouzid, the cradle of the revolution, where police fired teargas and warning shots at crowds who set cars and a police station on fire.
Mr Marzouki, who last month warned the tension between secularists and Islamists might lead to "civil war", has cut short a visit to France and cancelled a trip to Egypt scheduled for today.
While Mr Belaid's nine-party Popular Front bloc has only three seats in the constituent assembly, the opposition jointly agreed to pull its 90 or so members out of the body, which is acting as parliament and writing the new post-revolution charter. Ennahda and its allies have some 120 seats.
Tunisia was the first Arab country to oust its leader and hold free elections as uprisings spread around the region in 2011, leading to the ousting of regimes in Egypt, Yemen and Libya and to the civil war in Syria.
However, many who campaigned for freedom from repression under autocratic rulers and better prospects for their future feel their revolutions have been hijacked by Islamists they accuse of clamping down on personal liberties, with no sign of new jobs or improvements in infrastructure.
Tunisia's new constitution will pave the way for new elections but will inevitably be a source of friction between secularists and Islamists. The ruling parties have agreed to hold the vote in June, but that date still needs approval by the assembly.
Since the uprising, the government has faced a string of protests over economic hardship and Tunisia's future path, with many complaining hardline Salafists were taking over the revolution in the former French colony once dominated by a secular elite under the autocratic rule of Zine al Abidine Ben Ali.
Last year, Salafist groups prevented concerts and plays from taking place in Tunisian cities, saying they violated Islamic principles. That worries the secular-minded among the 11 million Tunisians, who fear freedom of expression is in danger.
Salafists also ransacked the US embassy in Tunis in September, during protests over an internet video mocking Islam.