As leader of the most powerful democracy, he defended the rights of newspapers to print what they see fit. But he felt obliged to tell the news media they must be sensitive about their power to offend.
That said, Mr. Bush called on foreign governments to bring a halt to the deadly rioting that has burned across the Muslim world in response to the publication of cartoons of the Prophet Muhammad.
The wall-climbing, gate-busting flag-burning protests further intensified Wednesday. In Afghanistan, police killed four demonstrators, part of a group moving toward a U.S. Military base, reports CBS News White House correspondent Jim Axelrod.
Mr. Bush's secretary of state, Condoleezza Rice, accused Syria and Iran of trying to inflame the situation.
The president spoke out about the controversy for the first time, signaling deepening White House concern about violent protests stemming from the publication of caricatures in Denmark's Jyllands-Posten and reprinted in European media and elsewhere in the past week.
"We reject violence as a way to express discontent with what may be printed in a free press," the president said.
At the same time, Mr. Bush admonished the press that its freedom comes with "the responsibility to be thoughtful about others."
Mr. Bush commented alongside King Abdullah II of Jordan at the White House. Abdullah, too, called for protests to be peaceful, but he also spoke against ridicule of Islam's holiest figure.
"With all respect to press freedoms, obviously anything that vilifies the Prophet Muhammad, peace be upon him, or attacks Muslim sensibilities, I believe, needs to be condemned," the king said.
In Afghanistan, meanwhile, police killed four people as protesters marched on a U.S. military base.
CBS News correspondent Sheila MacVicar reports U.S. officials are continuing to examine if there's a pattern of global incitement.
At the State Department, Rice said, "Iran and Syria have gone out of their way to inflame sentiments and to use this to their own purposes. And the world ought to call them on it."
There is little doubt that there is genuine anger throughout the Muslim world, where images of the revered Prophet Muhammad with a bomb strapped to his head are considered racist and deeply insulting.
In the post-Sept. 11 world, Muslims already feel the brunt of the war on terror and the invasions of Iraq and Afghanistan, said Diaa Rashwan, with the Al-Ahram Center for Political and Strategic Studies in Cairo, Egypt.
"That only further fueled the anger this time around," he said, the cartoons releasing bottled-up anger and frustration.
"Extremists are, of course, taking advantage of this situation to kind of strengthen their message and recruit more people to their message," said Radwan Masmoudi from the Center for the Study of Islam and Democracy. "And their message, of course, is that the west and Europeans and Americans are against Islam and this is a war against Islam and not just against terrorism."
In Afghanistan, U.S. military spokesman Col. James Yonts said, "Other countries are having the same demonstrations, same problems," when he was asked if al Qaeda and the Taliban may have been involved.
And Zahor Afghan, editor of Erada, Afghanistan's most respected newspaper, said that "there are definitely people using this to incite violence against the presence of foreigners in Afghanistan."
On Tuesday, Mr. Bush had called Denmark's prime minister to express "our support and solidarity" in the wake of the violence.
As for how the protests over the cartoon may affect American soldiers in Iraq, commanders tell CBS News correspondent Kimberly Dozier they want to further prove to Iraqis that they can be culturally and religiously sensitive and give people one less excuse to attack.
In the midst of a campaign to blunt widespread anti-American sentiment across the Mideast, Mr. Bush sought to balance his remarks by urging the media to be sensitive to religious beliefs.
"We believe in a free press," the president said. "We also recognize that with freedom comes responsibilities. With freedom comes the responsibility to be thoughtful about others."
Sitting alongside him, Jordan's Abdullah said, "Islam, like Christianity and Judaism, is a religion of peace, tolerance, moderation."
Mr. Bush said the furious reaction to the publication of the cartoons "requires a lot of discussion and a lot of sensitive thought."
"I first want to make it very clear to people around the world that ours is a nation that believes in tolerance and understanding," the president said. "In America we welcome people of all faiths.
"One of the great attributes of our country is that you're free to worship however you choose in the United States of America," the president said.
Islam is interpreted to forbid any illustrations of Muhammad for fear they could lead to idolatry.