The principle of freedom of expression "must not be infringed," Foreign Minister Laurent Fabius said, speaking on France Inter radio.
But he added: "Is it pertinent, intelligent, in this context to pour oil on the fire? The answer is no."
Anger over the film "Innocence of Muslims" has fueled violent protests from Asia to Africa. In the Lebanese port city of Tyre, tens of thousands of people marched in the streets Wednesday, chanting "Oh, America, you are God's enemy!"
Worried France might be targeted, the government ordered its embassies, cultural centers, schools and other official sites to close on Friday the Muslim holy day in 20 countries. It also immediately shut down its embassy and the French school in Tunisia, the site of deadly protests at the U.S. Embassy last week.
The French Foreign Ministry issued a travel warning urging French citizens in the Muslim world to exercise "the greatest vigilance," avoiding public gatherings and "sensitive buildings."
The controversy could prove tricky for France, which has struggled to integrate its Muslim population, Western Europe's largest. Many Muslims believe the Prophet Muhammad should not be depicted at all even in a flattering way because it might encourage idolatry.
Violence provoked by the anti-Islam video, which portrays the prophet as a fraud, womanizer and child molester, began with a Sept. 11 attack on the U.S. Embassy in Cairo, then quickly spread to Libya, where an attack on the U.S. Consulate in Benghazi left the U.S. ambassador and three other Americans dead.
In Washington, White House spokesman Jay Carney said the Obama administration believed the French magazine images "will be deeply offensive to many and have the potential to be inflammatory."
"We don't question the right of something like this to be published," he said, pointing to the U.S. Constitution's protections of free expression. "We just question the judgment behind the decision to publish it."
In a statement, Arab League chief Nabil Elarabi called the cartoons "provocative and disgraceful" and said their publication added complexity to an already inflamed situation. He said the drawings arose from ignorance of "true Islam and its holy prophet."
A lawsuit was filed against Charlie Hebdo hours after the issue hit newsstands, the Paris prosecutor's office said, though it would not say who filed it. The magazine also said its website had been hacked.
Riot police took up positions outside the magazine's offices, which were firebombed last year after it released an edition that mocked radical Islam.
Chief editor Stephane Charbonnier, who publishes under the pen name "Charb" and has been under police protection for a year, defended the cartoons.
"Muhammad isn't sacred to me," he told The Associated Press. "I don't blame Muslims for not laughing at our drawings. I live under French law. I don't live under Quranic law."
He said he had no regrets and felt no responsibility for any violence.
"I'm not the one going into the streets with stones and Kalashnikovs," he said. "We've had 1,000 issues and only three problems, all after front pages about radical Islam."
The cartoonist, who goes by the name Luz, also was defiant.
"We treat the news like journalists. Some use cameras, some use computers. For us, it's a paper and pencil," he said. "A pencil is not a weapon. It's just a means of expression."
A small-circulation weekly, Charlie Hebdo often draws attention for ridiculing sensitivity about the Prophet Muhammad. It was acquitted in 2008 by a Paris appeals court of "publicly abusing a group of people because of their religion" following a complaint by Muslim associations.
The magazine has staked out a sub-genre in France's varied media universe with its cartoons. Little is sacred, and Wednesday's issue also featured caricatures of people as varied as Clint Eastwood, an unnamed Roman Catholic cardinal who looked a bit like Pope John Paul II and French President Francois Hollande, a staple.
At the demonstration in Lebanon, Nabil Kaouk, deputy chief of Hezbollah's Executive Council, warned the United States and France not to anger Muslims.
"Be careful of the anger of our nation that is ready to defend the prophet," he said. "Our hearts are wounded and our chests are full of anger."
Nasser Dheini, a 40-year-old farmer, said instead of boosting security at its embassies, France should close down the offending magazine.
"Freedom of opinion should not be by insulting religions," said Dheini, carrying his 4-year-old son Sajed.
Outside the magazine's Paris offices, a passer-by wearing a traditional Muslim tunic said he was neither surprised nor shocked by the cartoons. He criticized France's decision to close embassies and schools for fear of protests by extremists.
"It gives legitimacy to movements that don't have any," said Hatim Essoufaly, who was walking his toddler in a stroller.
Report: 4 injured after explosion at kosher store
A French news agency is reporting that four people were injured when a small package bomb exploded inside a kosher grocery store in a Paris suburb.
The Sipa news agency says that the small explosion was set off by two hooded people dressed in black who entered the store around midday and put a package inside, citing an unnamed police official and a Jewish organization. The two fled after throwing a rock through the shop's window shortly before the explosion, the police official said. He spoke on condition of anonymity because he was not allowed to speak publicly about the investigation.
The official said the injured people are being treated for wounds to their arms and legs from the explosion and broken glass.
The attack took place in Sarcelles, a suburb about 12 miles north of Paris.
A French Jewish umbrella organization, CRIF, said in a statement that "it fears this attack" is connected to the days of violent protests from Asia to Africa against the U.S.-produced film "Innocence of Muslims," which ridicules Prophet Muhammad.
Other development Wednesday:
• The French Foreign Ministry issued a travel warning urging French citizens in the Muslim world to exercise "the greatest vigilance," avoiding public gatherings and "sensitive buildings."
• Several hundred lawyers protesting the movie forced their way into an embassy area in Pakistan's capital.
• The United States temporarily closed its consulate in an Indonesian city because of similar demonstrations.
• Hundreds protested the film in Sri Lanka's capital, burning effigies of President Barack Obama.