The twelve cartoons, which included a portrayal of the prophet wearing a time-bomb shaped turban, were printed last September in the daily paper Jyllands-Posten and re-printed earlier this month by a Norwegian Christian magazine.
Islam considers any image of the prophet blasphemous.
Danish flags have been burnt, products have been boycotted and threats of violence have been issued against Scandinavians in Muslim countries.
Both Jyllands-Posten and the Norwegian magazine have received bomb threats.
The paper's offices in both the town of Aarhus in central Denmark and in downtown Copenhagen were evacuated and searched with bomb-sniffing dogs Tuesday evening following the bomb threats.
After nearly two hours it was determined that the threat was a false alarm.
The paper has also reported that hackers had been trying to shut down its website, with more than 80,000 emails flooding the its inboxes, but said that technicians had managed to ward off the attack.
Diplomatic problems
The cartoons are also causing problems for Denmark’s international relationship with many Middle Eastern countries.
Saudi Arabia has recalled its ambassador to Denmark, Libya has shut down its embassy in Copenhagen, and on Tuesday, Iraqi Foreign Minister Hoshyar Zebari summoned Denmark's ambassador over the cartoons.
Interior ministers from 17 Arab countries called for the Danish government to "punish the authors" of the cartoons.
Thousands of Palestinians also demonstrated outside the United Nations compound in Gaza City burning a large picture of the Danish prime minister, while dozens of others demonstrated outside the Danish embassy in Tel Aviv.
"We are up against uncontrollable forces. It will take a huge effort to calm things down," Danish Prime Minister Anders Fogh Rasmussen told the media.
"Our diplomats are currently attempting to repair the misunderstandings that have surfaced," he added.
Danish Foreign Minister Per Stig Moeller met Tuesday with US Secretary of State Condoleezza Rice, UN Secretary General Kofi Annan and several of his Muslim counterparts at a conference in London to discuss the controversy.
Fatwa against Danish troops
The cartoon is also having an impact against Danish troops stationed in Iraq, with the Danish defence ministry saying a fatwa has been issued against the soldiers.
"I can confirm that we've heard about the fatwa from a reliable source in Iraq ... so we believe it's true," the Defence Minister’s spokesman Jacob Winther said.
Denmark has 530 soldiers in Iraq, mainly stationed in the south under British command.
Mr Winther said the troops had now been put on higher alert, but that the military did not yet know how worried to be.
"We don't know what kind of a fatwa it is, whether it's just a religious ruling of a death threat or what it is," he said, adding: "I don't think it's good."