Mr. Bush cited Turkey as an example of an Islamic country with a secular government that has found a place in the community of democracies.
"In some parts of the world, especially in the Middle East, there is wariness toward democracy, often based on misunderstanding," the president said. "Some people in Muslim cultures identify democracy with the worst of Western popular culture and want no part of it."
He made his remarks in a speech prepared for delivery before ending a five-day trip to Ireland and Turkey.
Mr. Bush said nations attending the NATO summit, which closes here on Tuesday, have formally agreed to work together with nations of the broader Middle East to fight terrorism, control their borders and aid the victims of disaster. But he said more action was needed.
"We must strengthen the ties of trust and good will between ourselves and the peoples of the Middle East," Mr. Bush said. "And trust and good will come more easily when men and women clear their minds and their hearts of suspicion and prejudice and unreasoned fear."
Mr. Bush believes democracy can flourish in Muslim countries, just as it has in Turkey. He said that supporting freedom and democracy in volatile nations will help secure America and other countries too.
But Mr. Bush's initiative has been criticized by some Arab leaders, who accuse the United States of trying to export its brand of democracy while not doing enough to resolve the Israeli-Palestinian conflict. Some also see hypocrisy in the U.S. pressuring Iran, where some leaders are elected, while allying itself with Saudi Arabia, a monarchy.
Mr. Bush was to deliver his speech at a state-run university here near the historic Bosporus Bridge that has long linked Europe and Asia. He said Turkey, a democracy with a secular government and the only Muslim nation that is in NATO, was a model for the region, and he reiterated his backing of Turkey's desire to join the European Union.
"Including Turkey in the EU would prove that Europe is not the exclusive club of a single religion, and it would expose the 'clash of civilizations' as a passing myth of history," Mr. Bush said.
Monday, French President Jacques Chirac said Mr. Bush had overstepped by wading into EU's affairs with his call for Turkey's admission. Chirac said that Mr. Bush commenting on Turkish-EU relations was like a French leader commenting on U.S.-Mexican ties. The relationship between the two leaders was strained by the war in Iraq, which France opposed.
Also Tuesday, in an impassioned speech, Afghan President Hamid Karzai pleaded for the alliance not to wait till the fall elections to send extra troops to his country, reports CBS News White House Correspondent Mark Knoller.
"Please hurry," Karzai said. "Come sooner than September and provide the Afghan men and women with a chance to vote freely without fear, without coercion."
On Monday, the alliance decided to expand its peacekeeping forces in Afghanistan from 6,500 to 10,000 over the election period, although officials clarified Tuesday that about 1,300 of those troops will be held in reserve outside the country for emergency use.
The expanded NATO forces should allow the separate, 20,000-strong U.S.-led force to intensify its focus on pursuing insurgents from the old Taliban regime and its al Qaeda allies in the troubled south and east, but it has been criticized as insufficient. NATO troops have mostly confined their operations to the capital, Kabul.
Although the alliance agreed in October to expand the force, it has been unable to persuade governments to provided the necessary troops, apart from a small German force based in the northern city of Kunduz.
The months of delays have cast doubt on the alliance's credibility as is seeks to reinvent itself as a global security force for the post-Cold War era.
"It's a disgrace," said Jon Sifton, a researcher at Human Rights Watch. "NATO officials should be ashamed … If these elections fail to occur, or occur but are not free and fair, Afghans can blame NATO."
He said Afghanistan had been neglected while western leaders were focused on Iraq. NATO leaders on Monday agreed to help train the armed forces there.
Karzai thanked the 26 NATO leaders for expanding the force, then made a forceful plea for an accelerated deployment, reminding the summit ofon officials carrying out voter registration and on registered voters.
"The Afghan people have trust in the security that you are going to provide for us, but the Afghan people need that security today and not tomorrow," he said.
"The reason we need this is that we have three challenges still in our country. First the challenge of terrorism, as you are all aware, second is the challenge of private militias … third is the challenge of narcotics," he said.
Outside the summit, police fired tear gas to break up a demonstration, the second day in a row that police have clashed with protesters.
Around 1,000 protesters took part in the protest. Several protesters were detained.
News reports said shop windows were shattered after police refused to allow the protesters to march to nearby Taksim square, Istanbul's main square, which is off-limits to protesters.
The demonstrators said they were protesting police intervention in protests on Monday, when police also used gas to prevent the protesters from marching toward the summit area.