French schools in Tunisia closed for four days on Wednesday and the embassy requested extra security, after the publication in France of cartoons the ruling Islamists branded a "new attack" on the Prophet Mohammed.
Tunisia's Ennahda party said Muslims have "the right to protest" against the publication of the cartoons mocking the Prophet, as long as they do so peacefully.
"Ennahda backs the right of Muslims to protest and calls on the use of peaceful and civilised means," the Islamist party that leads the governing coalition in Tunis said in a statement.
It branded French weekly Charlie Hebdo's publication of cartoons of Mohammed, some of which portray him naked, as "a new attack against the Prophet."
Amid heightened security concerns, the French embassy announced the temporary closure of French schools in the former colony, said it had requested extra security around the mission and appealed for vigilance.
The controversial images published on Wednesday come against a background of violent protests across the Muslim world, which first erupted early last week over an anti-Islam film made in California and posted on the Internet.
Four people were killed and dozens wounded on Friday during a demonstration by hardline Salafists outside the US embassy in Tunis, with protesters hurling petrol bombs and storming the mission, while police fired live rounds and tear gas.
"In the current context, the French community is urged to be vigilant, to avoid all public gatherings and to stay away from sensitive areas," the embassy said.
"The French school network and Tunisia's French Institute will be closed from midday on Wednesday... until Monday morning."
"The embassy has asked the relevant Tunisian authorities to strengthen security around its sites," it said, adding that the mission would stay closed on Friday, when Islamist protests following weekly prayers are common.
Unlike most Arab countries, Tunisia follows the Western weekend, meaning that Thursday and Friday are normal working days.
"It's a preventative measure. We have not received any direct threats," an embassy source told AFP.
There are an estimated 30,000 French citizens living in Tunisia and around 3,000 French children enrolled in Tunisian schools.
Earlier the French foreign ministry in Paris said France would close its embassies and schools in around 20 countries on Friday because of fears of being targeted by angry Muslim protesters after the publication of the cartoons.
Also on Wednesday, US ambassador Jacob Walles met Prime Minister Hamadi Jebali and asked him to guarantee the security of US interests in the country, amid strong criticism of the security forces for their handling of Friday's protest.
The United States has already evacuated all non-essential embassy staff and family members from Tunisia.
Tunisia's Interior Minister, Ali Larayedh, was questioned by the National Constituent Assembly over the response to Friday's unrest, amid calls for him to quit by numerous opposition MPs.
In Paris, police were deployed outside the offices of Charlie Hebdo, the satirical magazine which printed the cartoon series of the Prophet Mohammed.
The left-wing, libertarian publication's offices were firebombed last year after it published an edition "guest-edited by Mohammed" that it called Sharia Hebdo.
French Prime Minister Jean-Marc Ayrault urged "responsibility" and said anyone offended by the caricatures could sue, but made it clear that France would take no action against the weekly.
He and Interior Minister Manuel Valls said freedom of speech, including caricature, was a "fundamental right" backed by the law.
Leaders of the large Muslim community in France said an appeal for calm would be read out in mosques across the country on Friday but also condemned the magazine for publishing "insulting" images.