Spontaneous renditions of "Happy Birthday" erupted among a South Lawn crowd estimated between 9,000 and 12,000 to mark the pontiff's 81st birthday.
Accompanied only by a harp, soprano Kathleen Battle sang "The Lord's Prayer."
Bush said Pope Benedict would find the U.S. "a nation of prayer."
The president said "Millions were praying for your visit and millions look forward to praying with you this week."
The pope said the United Sates "traditionally has shown herself as generous in meeting human need."
Catholics in America, he said, "have made and continue to make an excellent contribution" to society.
After the public ceremony ended, the pope and the president exited to the White House, emerging from the Blue Room balcony.
An "official" version of "Happy Birthday" was played and sung.
After the ceremony, Pope Benedict traveled -- slowly amid the cheering throngs -- to the Vatican embassy via the custom-made, bullet-proof "pope-mobile."