Anders Fogh Rasmussen said that the next step in the crisis will by carried out at a European level in coordination with the EU.
"This affair is not just an issue between Denmark and the Muslim world. It has to a much greater degree evolved into an affair between the European Union and the Muslim world," Mr Rasmussen told reporters in Copenhagen.
The caricatures were first printed in the Danish daily Jyllands-Posten last September, but were later re-published by papers in other European countries. However Muslim outrage over the cartoons has been mainly leveled at Denmark.
His statements came as Danish diplomats returned to Indonesia after they were recalled at the height of the violent uproar in that country. The Danish consulate in Tunisia has also reopened.
Attempting to ease tensions
The chief of the Organisation of the Islamic Conference (OIC), Ekmeleddin Ihsanoglu, rejected a fatwa or religious decree issued by an Islamic court in India that condemned the cartoonists to death.
"It is very dangerous, personal fatwas like this harm our cause," Mr Ihsanoglu said.
"This fatwa is a wrong fatwa. Nobody should adhere to it because it goes against the essence of Islam and the prophet's teachings. Nobody has the authority to kill anybody," he said.
In a separate incident a Pakistani cleric on Friday offered a one-million-dollar reward for the deaths of the artists.
Prime Minister Rasmussen said that Denmark had taken the "necessary measures" to protect the cartoonists.
Mr Rasmussen and his foreign minister, Per Stig Moeller blamed extremist elements for continuing to incite anger over the cartoons in order to serve their own purposes.
"It is obvious to everybody that this crisis no longer just concerns these12 drawings in Jyllands-Posten. It is now about completely different goals being pursued in the Muslim world," Mr Rasmussen said.
The Prime Minister has rejected the opposition's calls for an independent inquiry into the government's role.