Denmark's Jyllands-Posten newspaper, which published the cartoons, issued an apology late on Monday in a statement to Arab countries, sent to the Jordanian news agency Petra.
The drawings, which seemed to portray the prophet as a terrorist, were published in September, but the row erupted this month after diplomatic efforts to solve the issue failed. One drawing shows Prophet Muhammad wearing a turban shaped as a bomb.
Muslims deem images of prophets disrespectful and caricatures blasphemous, and some have threatened Danes and demanded an apology.
The newspaper said in a statement: "The drawings are not against the Danish law but have indisputably insulted many Muslims, for which we shall apologise."
Iraqi fighters' threat
An Iraqi fighters' group called on Monday for attacks on Danish and Norwegian targets, according to a statement attributed to the Mujahidin Army. A Norwegian paper has also run the drawings.
The internet statement called on fighters to "hit whatever targets possible belonging to these two countries and others that follow their steps". It could not be authenticated.
Denmark has about 530 troops serving in Iraq.
Denmark has about 530 troops
deployed in Iraq
A roadside bomb exploded near an Iraqi police car driving in front of a Danish forces patrol, wounding one Iraqi, the Danish army said on Monday, adding it had no reason to conclude the attack was connected to the cartoon row.
As the diplomatic and economic impact has spread, Saudi Arabia has recalled its envoy from Denmark and its religious leaders called for a boycott of Danish products.
Across the Gulf, several supermarkets pulled Scandinavian foods off the shelves after consumers complained.
Sudan said it had told a Danish government minister he could not make a planned visit and said it had also called for a boycott of Danish goods.
Jamal Ibrahim, a Sudanese Foreign Ministry spokesman, said: "This is an insult to the Prophet Muhammad. Furthermore, we have asked our national companies to boycott all Danish goods."
Libya has closed its Copenhagen embassy, and thousands of Palestinians marched in protest on Monday.
Anders Fogh Rasmussen, Denmark's prime minister, welcomed the paper's statement but did not apologise.
Supermarkets across the Gulf are
no longer selling Danish products
Rasmussen said: "The Danish government cannot apologise on behalf of a Danish newspaper. It does not work like that ... and we have explained that to the Arab countries. Independent media are not edited by the government."
Earlier on Monday, he advised colleagues in the European Union of the situation and the bloc's executive said it might complain to the World Trade Organisation about the boycott if the Saudi government had encouraged it.
The Danish Foreign Ministry advised against non-essential travel to Saudi Arabia and urged Danes to be cautious in other Muslim countries.
"Danes who choose to stay in Saudi Arabia should show extraordinarily high watchfulness," it added on its website.
The Danish Red Cross said it had pulled two employees out of Gaza and one from Yemen, and Norway's Foreign Ministry said two Norwegian aid workers in Gaza were planning to leave on Monday.
Sweden warned its citizens against travelling to Gaza and the West Bank and the Swedish consulate in Jerusalem received a fax claiming to be from Fatah's al-Aqsa Martyr's Brigades demanding that all Danes and Swedes should leave the area.
"All Swedes and Danes that exist on our soil have 48 hours to leave our country or else," according to the fax read to Reuters by a consulate official.
Dozens of Palestinians with rifles and grenade launchers rallied outside the EU headquarters in Gaza City, demanding an apology and warning Danes and Norwegians they would be at risk in Gaza.
Palestinians protested outside
the EU headquarters in Gaza
Some of the armed men fired in the air, while others burned Danish and Norwegian flags.
Hamas, the Islamic resistance group which won Palestinian elections last week, urged Muslim countries to take "deterrent steps against idiotic Danish behaviour".
Hardest hit by the boycott was Danish-Swedish dairy product maker Arla Foods, with annual sales of $487 million in the Middle East. The world's biggest maker of insulin, Novo Nordisk, also said it was affected.