French President Jacques Chirac has condemned as "overt provocation" decisions to reprint cartoons satirising the Prophet Muhammad.
Charlie Hebdo magazine has sold out in many newsagents
As another French publication printed the cartoons, Mr Chirac said any subject matter that could hurt other people's convictions should be avoided.
But Denmark's PM said it was not for the government to censor the media.
Meanwhile protests at the cartoon's publication continued, with four killed and up to 20 injured in Afghanistan.
The deaths - at a protest by about 400 people in the town of Qalat - bring to 12 the number of people killed in Afghan protests over the cartoons in recent days.
Afghanistan's top council of Muslim clerics has called for an end to several days of demonstrations.
US President George W Bush urged governments to prevent attacks on diplomatic missions.
"I call upon the governments around the world to stop the violence, to be respectful, to protect property, protect the lives of innocent diplomats who are serving their countries overseas," he said.
He also criticised anything that vilified Muhammad or attacked Muslim sensibilities.
The BBC's Jonathan Beale in Washington says the Bush administration has carefully avoided taking sides in the row over the cartoons, because of concerns that the issue could further fuel anti-American sentiment in the Arab world.
In other developments:
- Hackers attack hundreds of Danish websites, posting pro-Islamic messages condemning publication of the images
- Several hundred people march on the Italian embassy in the Bangladeshi capital Dhaka, but are blocked by police
- About 300 Palestinian protesters attack an international observers' mission in the West Bank town of Hebron, throwing rocks and bottles and trying to torch one of its buildings
- Thousands demonstrate in Pakistan's Dara Adam Khel tribal region, bordering Afghanistan
- The United Nations, the Organisation of the Islamic Conference and the European Union issue a joint statement calling for restraint from all sides.
President Chirac said freedom of expression was one of the foundations of the French republic but should not be abused. He called for tolerance and for all beliefs to be respected.
30 Sept 2005: Danish paper publishes cartoons
20 Oct: Muslim ambassadors complain to Danish PM
10 Jan 2006: Norwegian publication reprints cartoons
30 Jan: Gunmen raid EU's Gaza office demanding apology
1 Feb: Papers in France, Germany, Italy and Spain reprint cartoons
4 Feb: Danish and Norwegian embassies in Damascus attacked
5 Feb: Protesters set alight Danish embassy in Beirut
6-7 Feb: At least eight killed in protests in Afghanistan
"Anything that can hurt the convictions of another, particularly religious convictions, must be avoided," he said. "Freedom of expression must be exercised in a spirit of responsibility.
"I condemn all manifest provocation that might dangerously fan passions."
But Danish Prime Minister Anders Fogh Rasmussen told the BBC it was up to the media to decide what they should publish.
"The government cannot interfere with the media," he said. "But I think these events have stressed the importance of combining freedom of expression with respect for religious beliefs."
The latest magazine to publish the cartoons, Charlie Hebdo, won the backing of a French court on Tuesday, after several Islamic organisations had complained that publication would amount to an insult to their religion.
New print run
The magazine features all 12 cartoons of Muhammad that originally appeared in a Danish paper last year - including one that shows Muhammad with a bomb-shaped turban.
Religions other than Islam are caricatured as well.
The magazine says copies have been selling so fast it is considering another print run.
The BBC's Alasdair Sandford in Paris says the newsagents he visited had it discreetly turned face down.