In a statement, Annan said he shared the "distress" of many Muslims at the publications of the cartoons, first published in Denmark in September and recently reprinted mainly in Europe.
But Annan said such resentment cannot justify violence, least of all when it is directed against people who have no responsibility for or control over the publications in question.
On 5 February, thousands of angry Muslims set fire to the Danish Embassy in Beirut, prompting the country's interior minister to resign.
On 4 February, thousands of protesters destroyed the Danish and Norwegian embassies in Damascus.
The European Union has condemned the violence as "utterly unacceptable."
(dpa)