Anders Fogh Rasmussen said on Thursday: "I would not rule out the idea that, at the end of the day, the solution to the crisis will be found at the UN."
He told reporters after a meeting of parliament's foreign policy committee that he still favoured a Europe-led solution to the crisis, noting that the crisis between Denmark and the Muslim countries had evolved into a matter for the European Union.
EU foreign ministers were likely to discuss the matter on Monday, he said, calling European cooperation in the case "precious".
Rasmussen once again rejected the centre-left opposition's call for an independent investigation into the government's role in the affair, seen as the Scandinavian country's most serious crisis since World War II.
The opposition had repeated their call for a probe earlier in the day after a report that Egypt had offered to help Denmark several times since October to avoid the crisis, only to be turned down by Per Stig Moeller, the Foreign Minister .
"I would not rule out the idea that, at the end of the day, the solution to the crisis will be found at the UN"
Anders Fogh Rasmussen,
Danish Prime Minster
Rasmussen has refused to apologise for the publication of the cartoons, insisting that his government has no say over what appears in the media in Denmark.
Ahmed Aboul Gheit, the Egyptian Foreign Minister, told the Politiken daily that he had warned Moeller that the cartoons "could cause problems for your country with the rest of the Arab-Muslim world. I warn you, we must find a solution before these problems arise".
"I said that we were approaching something that was very dangerous. The contents of this case risked causing serious consequences". Gheit recalled.
Moeller had replied that the warnings were not needed, according to Gheit.
The Politiken article contained "nothing new", Rasmussen said on Thursday.
A dozen drawings of the Prophet Muhammad first appeared in Danish daily Jyllands-Posten last September, sparking violent protests in Muslim countries over the past month against Denmark and several other European countries where the cartoons have since been reprinted.