"I would never myself depict any religious figure, including the Prophet Muhammad, in a way that could hurt other people's feelings," he said during the Alliance of Civilisations forum, a conference sponsored by Turkey and Spain to promote understanding between the Muslim world and the west.
"I was deeply distressed that the cartoons were seen by many Muslims as an attempt by Denmark to mark and insult or behave disrespectfully towards Islam or the Prophet Muhammad. Nothing could be further from my mind," Rasmussen said.
Remorse over cartoons
The twelve cartoons that were published in Jyllands-Posten led to attacks on Danish and Western embassies and boycotts of their products.
Islamic law generally prohibits any depiction of the prophet for fear that it may lead to idolatry.
In anticipation of his speech, the Turkish media had reported that Rasmussen would apologise for his previous position of defending Jyllands-Posten's right to publish the cartoons.
In the event, Rasmussen expressed remorse and disappointment, but was careful not to apologise, citing the sanctity of freedom of speech and his government's inability to be responsible for the actions of Denmark's free press.
Rasmussen also responded to Turkish requests to ban a Denmark-based channel that they accuse of being a mouthpiece of the Kurdistan Workers' Party (PKK).
The PKK is listed as a terrorist organisation by the European Union but Rasmussen said that he would not examine the legal grounds for closing the channel unless the station was proven to have links to terrorists.
Turkey's initial opposition to Rasmussen's appointment had threatened the image of unity at Nato's 60th anniversary summit in the French city of Strasbourg.
The dispute was resolved after Barack Obama, the US president, guaranteed that Turkish commanders would be present at the Nato's command and that a Turk would be appointed as one of Rasmussen's deputies.
Recep Tayyip Erdogan, Turkey's prime minister, opened the conference with a speech that called for renewed efforts to overcome religious and cultural divisions.
"We still have the opportunity to write the history of this century, which we began with conflict and polarisation based on religious and cultural differences, as one of peace, harmony and tolerance," he said.
The conference was also attended by Ban Ki-moon, the UN secretary-general.