Tunisia's opposition has called for a nationwide strike to protest about the murder of prominent anti-Islamist politician Chokri Belaid.
Mr Belaid was shot in the neck and head in the capital, Tunis, in the first political assassination since the Arab Spring uprising of January 2011.
Police fired tear gas to disperse thousands of people protesting against his killing in Tunis and other towns.
The army has been deployed in Sidi Bouzid, the revolution's birthplace.
The Islamist-led government said Mr Belaid's murder was an "odious assassination".
President Moncef Marzouki said he was cutting short a visit to France and cancelling a trip to Egypt to return home to deal with the crisis.
Mr Belaid was a respected human rights lawyer, and a left-wing secular opponent of the government which took power after the overthrow of long-serving rule Zine el-Abidine Ben Ali.
The Popular Front (PF), a coalition of opposition groups of which Mr Belaid was a member, said it was calling for a nationwide strike on Thursday to protest against his assassination.
The BBC's Sihem Hassaini in Tunis says most people are likely to heed the call for the strike as the main Islamist party in government, Ennahda, is deeply unpopular at the moment.
Many offices, universities and schools are expected to stay closed, she says.
The PF also said it was pulling out of the Ennahda-dominated parliament, which has been battling to draft a new constitution for Tunisia.
The parliament would be suspended on Thursday to mourn Mr Belaid's death, the official news agency Tap reports.
The decision indicates that Ennahda wants to show solidarity with Mr Belaid's family and supporters, who are blaming it for his killing, our reporter says.
Speaking in front of the European Parliament on his visit to Strasbourg, President Marzouki said the murder of Mr Belaid should not affect Tunisia's revolution.
"There are many enemies of our peaceful revolution. And they're determined to ensure it fails," he said.
Referring to Mr Belaid as a "long-standing friend", he said his "hateful assassination" was a threat.
"This is a letter being sent to us that we will refuse to open," the president said.
Residents in Sidi Bouzid told our correspondent that police have been withdrawn from the town after young protesters torched a police station.
The army has now been deployed to maintain order in Sidi Bouzid, the town where the revolution that toppled Ben Ali began a little more than two years ago, our reporter says.
According to AFP news agency, people torched the premises of the Ennahda party in the central town of Mezzouna, and ransacked the party's offices in the mining town of Gafsa in protest at Mr Belaid's death.
In Tunis, police fired tear gas to disperse protesters who had gathered outside the interior ministry.
Crowds had been chanting they want a "second revolution" and surged towards the ambulance carrying Mr Belaid's body as it drove through the city centre, our correspondent says.
It is not known who is responsible for the attack on the politician.
Prime Minister Hamadi Jebali said his murder was an "act of terrorism" and promised to pursue all efforts to "immediately" arrest the murderer.
Mr Belaid was the co-ordinator of the left-leaning Democratic Patriots (DP) party, which is part of the PF coalition which has been challenging the government since it came to power following the country's first post-Arab Spring election in October 2011.
"This murder robs Tunisia of one of its most courageous and free voices," French President Francois Hollande said in a statement.
On Saturday, Mr Belaid accused "mercenaries" hired by Ennahda of carrying out an attack on a DP meeting.
"My brother was assassinated. I am desperate and depressed," Mr Belaid's brother Abdelmajid Belaid told AFP.
Correspondents say that although Mr Belaid's party did not have a large share of the election vote, it spearheaded popular concern over the rising level of political violence in Tunisia.