Stephane Dujarric, the UN's chief spokesman, said on Thursday: "He (Annan) believes that the freedom of the press should always be exercised in a way that fully respects the religious beliefs and tenets of all religions."
Annan also believed "in the importance of overcoming misunderstandings and animosities between people of different beliefs and cultural traditions through peaceful dialogue and mutual respect," Dujarric said.
The Danish daily Jyllands-Posten, which printed the cartoons last September, has apologised for causing offence, but stood by the decision to print them.
One of the drawings shows the Prophet wearing a bomb-shaped turban.
Dujarric said: "The secretary-general is concerned over the controversy that has been created by the publication of the Danish cartoons."
Newspapers in France, Germany, Spain, Switzerland and Hungary reprinted the caricatures this week, saying press freedom was more important than the protests and boycotts they have provoked.
But many Muslims saw the cartoons as deliberate provocation. Anger against the cartoons has led to a boycott of Danish goods in several Middle Eastern countries.