The cartoons, first published in Denmark, caused outrage in the Muslim world, and Danish and other European diplomatic missions have been attacked in Syria, Lebanon, Iran, Pakistan and Indonesia.
Political leaders from all groups rallied behind Copenhagen in a special debate in the European Parliament, declaring that an attack on Denmark was an attack on all member states and condemning the resort to violence by some protesters.
However, libertarians warned against any attempt to make the media adopt self-censorship.
"I want here today to send my solidarity to the people of Denmark," European Commission President Jose Manuel Barroso said, calling Danes "a people who rightly enjoy the reputation as being amongst the most open and tolerant not just in Europe but in the world".
Danish goods have been subject to boycotts in some Muslim countries, and Barroso was applauded when he said such action was by definition a boycott of European goods.
Greens leader Daniel Cohn-Bendit condemned companies such as French hypermarket chain Carrefour and Swiss food giant Nestle for issuing notices in Muslim countries saying they were not Danish or did not stock Danish goods.
He and liberal spokeswoman Karen Riis-Joergensen urged the European Commission to drop the idea of encouraging the media to adopt a voluntary code of conduct that would avoid offending religious sensibilities.
"If we start undermining freedom of expression, our right to analyse any religion critically, our fundamental right to speak freely and express ourselves will be violated," Riis-Joergensen said.
Heinz Fischer (R) called
for media self-restriction
However, Austrian President Heinz Fischer, whose country holds the EU's rotating presidency, appeared in an address to the EU legislature to call for media self-restriction.
"If a ban on pictorial representation constitutes an essential element of a religion, one ought not and must not offend against this principle twice - not only by disrespecting this ban, but also by reinforcing this hurtful violation of a taboo in the form of a caricature," he said.
Islamic tradition forbids depicting the prophet.
The leader of the centre-right European People's Party, Hans-Gert Poettering, called for a commission of experts chosen by the EU and the Organisation of the Islamic Conference to review schoolbooks for ethnic and religious prejudice.
Brandishing magazines published in Muslim countries, he said: "We have documents of hundreds of cartoons and caricatures which make a mockery of our values and our religion. So these cartoons exist in the Islamic world too."
Danish embassies have been
attacked by protesters
The socialist and liberal groups each symbolically chose a Danish EU member as its speaker in the debate.
Poul Nyrup Rasmussen, the Socialist former prime minister of Denmark, said he was shocked to see people attacked, flags burned and embassies damaged.
He criticised his centre-right successor, Anders Fogh Rasmussen, the prime minister, for refusing to meet ambassadors from Muslim countries when they asked to see him last year after the cartoons were first published.
Fogh Rasmussen was quoted in Algeria's al-Watan newspaper on Wednesday as saying he, too, was horrified to see Danish diplomatic missions attacked.
"All countries have an obligation to ensure the security of diplomatic missions on their territory," he said, adding that Iran and Syria had failed in that obligation.
Parliament leaders, the European Commission and the Austrian EU presidency vowed to strengthen dialogue with moderate Muslims and not to let extremists disrupt their relations.
"Extremists cannot be allowed to triumph," said Hans Winkler, the Austrian State Secretary for Foreign Affairs. EU foreign ministers would take new steps to strengthen dialogue at their next meeting on 27 February, he added.