Accusing "radicals, extremists and fanatics" of fanning the flames of Muslim wrath to "push forward their own agenda", he repeated a call for dialogue with offended Muslims.
"I want to appeal and reach out to all people and countries in the Muslim world. Let us work together in the spirit of mutual respect and tolerance," he said.
Rasmussen received a call of support from George Bush, the US president, and the backing of European Union allies, but there was no sign of the row abating.
Protests in Muslim countries over the offending cartoons have led to violent clashes, resulting in the deaths of at least 10 people in Afghanistan, Lebanon and Somalia.
Danish products have been
boycotted in several countries
UN peacekeepers from Norway, which has also attracted Muslim wrath after a Norwegian paper reproduced the cartoons, were attacked by mob in Afghanistan, while people and buildings from other European nations were also attacked.
Rasmussem said this showed that "this is not a matter between the Muslim world and Denmark alone", but it was above all Danish embassies and flags being stoned and burnt by Muslims.
After Denmark's Iranian embassy was attacked for a second day, Per Stig Moeller, the Danish foreign minister, called on Tehran to protect foreign diplomats. The prime minister warned Iran that it could be blocked from joining the World Trade Organisation if it carried out a threatened Danish trade boycott.
Danish newspaper Jyllands-Posten has apologised for the cartoons published last September and the Danish government has tried to mollify Muslims without apologising for the newspaper.
The cartoonists have gone into hiding with police protection.
Some Danes fear the row has heightened the risk of a terrorist attack in Denmark, which has 530 troops in Iraq.
In a poll by Epinion for Danish radio, about four in 10 people said publication of the cartoons meant that there was now a serious risk of an attack. More than half said the gap between Muslim and non-Muslim Danes had widened because of the cartoons.
The cartoon row raised concerns for the safety of Danish troops in Afghanistan and in Iraq, though there are no plans to pull out.
"I want to appeal and reach out to all people and countries in the Muslim world. Let us work together in the spirit of mutual respect and tolerance"
Anders Fogh Rasmussen,
Danish prime minister
Soren Gade, the defence minister, said: "We have to change the patterns of how they patrol and take precautions to make sure we don't put them in danger." As well as troops in Iraq, Demark plans to double its 178-strong Afghan mission this year.
Gade also said Danish troops on UN peacekeeping missions in Muslim countries had changed into uniforms without the Danish flag for their own safety and aid workers in Pakistan had also removed the Danish flag from their camp.
Heeding security advice from their government, thousands of Danes cancelled plans to travel to the Middle East and Indonesia. Arla, a large Danish dairy company, has sent some workers home because of the Middle East boycott.
Fie Sandfeld of travel agency Star Tour said a dozen clients were being evacuated from Bali and about 3000 Danes had cancelled trips to Egypt, but most of those already abroad wanted to stay.
"We currently have 500 guests in Egypt and 200 in Morocco. We have offered to bring them home, but the vast majority are staying," Sandfeld said. "Only four from Egypt want to come home, otherwise we are hearing that things are calm and that they are not affected by the conflict."