Speaking in Washington after a meeting with Jordan's King Abdullah, Bush said press freedoms should be excercised with sensitivity, but added: "We reject violence as a way to express discontent with what may be printed in a free press".
"I call upon the governments around the world to stop the violence, to be respectful, to protect property, protect the lives of innocent diplomats who are serving their countries overseas," the US president said.
Earlier police in Afghanistan shot four protesters dead as a large crowd tried to march on the US military base at Bagram, north of the capital Kabul.
Islamic organizations too have called for an end to the deadly rioting across the Muslim world.
Eleven people have been killed in the last week in Afghanistan alone as thousands joined street protests across the country against the cartoons.
Violent protests also claimed lives in Lebanon and Somalia, with dozens reported injured in skimishes around Danish and European embassies.
Bush made his comments after a meeting with King Abdullah II of Jordan.
"We reject violence as a way to express discontent with what may be printed in a free press"
"With all respect to press freedoms, obviously anything that villifies the Prophet Muhammad ... or attacks Muslim sensibilities, I believe, needs to be condemned," the king said.
He went on to say that those who want to protest should "express their views peacefully".
"When we see protests, when we see destruction, when we see violence - especially if it ends up taking the lives of innocent people, (it) is completely unacceptable," he said.
"Islam is a religion pf peace, toleration and moderation", he added.
Bush, with King Abdullah said
"freedom" has responsibilities
Bush said that the reaction to the publication of the drawings was a subject "that requires a lot of discussion and a lot of sensitive thought.
The president also went on to say that he "recognized that with freedom comes responsibilities. With freedom comes the responsibility to be thoughtful about others".
The drawings - including one depicting the prophet wearing a turban shaped as a bomb - have stirred a furore among Muslims.
Islam forbids any illustrations of Muhammad.
The caricatures were first published in the Danish newspaper Jyllands-Posten in September last year.