Charlie Hebdo's editor defended his magazine's decision to publish the cartoons
Security is being stepped up at some of France's embassies after a French satirical magazine published obscene cartoons of the Prophet Muhammad, reports the BBC.
Foreign Minister Laurent Fabius said he was "concerned" after the issue of Charlie Hebdo appeared on news-stands.
French embassies, consulates, cultural centres and international French schools in some 20 countries will be closed on Friday as a precaution.
Riot police have been deployed around the magazine's offices in Paris.
The magazine has confirmed that its website has been attacked. It was not accessible as of Wednesday morning.
Its paper edition features caricatures which play on both the uproar in the Islamic world over an amateur video which mocks Islam and the row over the publication in France of topless photos of the Duchess of Cambridge.
A central tenet of Islam bans the portrayal of its founder, the Prophet Muhammad.
Some 30 people have died in violent protests which erupted early last week over the Innocence of Muslims video, which was made in the United States.
The dead include the US ambassador to Libya, Christopher Stevens, and three other Americans, who died in Benghazi. US and other Western embassies have come under attack in mainly Muslim countries.
Friday's closures relate to possible protests following weekly Muslim prayers.
While no list of countries affected was immediately available, the embassy in Jakarta announced on its website that it would close on Friday.
French schools in Tunisia were due to close from Wednesday afternoon until Monday morning.
A statement about the cartoons on the French foreign ministry's website quotes Prime Minister Jean-Marc Ayrault as saying "freedom of expression is one of [France's] fundamental principles", as are secularism and respect for religious convictions.
"And this is why, in the current context, the prime minister would like to express his disapproval of any excesses," the statement adds.
Muslim leaders urged calm in France, which has the EU's largest Muslim community - about 10% of the population.
"This is a disgraceful and hateful, useless and stupid provocation," Dalil Boubakeur, rector of the Paris Grand Mosque, told the Associated Press news agency.
"We are not like animals of Pavlov to react at each insult," he added, referring to the Russian physiologist who pioneered research into conditioning.
Boubakeur and other Muslim representatives are due to meet French Interior Minister Manuel Valls on Wednesday, French TV channel TF1 reports.
Charlie Hebdo, known in France for its scatological cartoons, has caricatured other religious figures in the past, including a "Pope special" in 2008 which resulted in an unsuccessful court action accusing the magazine of inciting hate.
One of the milder cartoons in Wednesday's edition, the cover image, shows an Orthodox Jew pushing a turbaned figure in a wheelchair, with the caption "You mustn't mock".
Among the explicit cartoons inside, one clearly parodies the topless photos of the Duchess of Cambridge which appeared in Closer magazine, and resulted in an injunction on Tuesday.
Magazine editor Stephane "Charb" Charbonnier said the images inside would "shock those who will want to be shocked".
"The freedom of the press, is that a provocation?" he asked.
"I'm not asking strict Muslims to read Charlie Hebdo, just like I wouldn't go to a mosque to listen to speeches that go against everything I believe."
In November, the magazine's offices in Paris were gutted by a petrol bomb attack after it named the Prophet Muhammad as its "editor-in-chief" for an issue.
During the protests against the Innocence of Muslims, a crudely produced film trailer made in the US, French police arrested some 150 people at an unapproved rally near the US embassy in Paris.