Before heading for Saudi Arabia, Bush attended a roundtable discussion with young Arab leaders.
"I'm most impressed by what I've seen here," Bush said, adding, "I also want you to understand something about America: that we respect you, we respect your religion and we want to work together for the sake of freedom and peace.
Dubai declared a public holiday for Bush's visit, part of a multi-country sweep of the Middle East to support the peace process.
All roads in the city-state were closed as Bush and his entourage were treated to cultural displays including young girls dancing to Arabic music.
The president then attended a roundtable of the Young Arab Leaders group at the Burj Al Arab Hotel, where he referred to the main purpose of his Middle East trip.
Dubai is a staunch U.S. ally and provides a port to U.S. military ships.
Bush was scheduled to depart for Saudi Arabia later Monday in the weeklong trip that began Wednesday in Israel.