Mr Bush said: "In a world where some no longer believe that we can distinguish between simple right and wrong, we need your message to reject this dictatorship of relativism."
He added: "In a world where some evoke the name of God to justify acts of terror and murder and hate, we need your message that God is love."
Such a message would "save man from falling prey to the teaching of fanaticism and terrorism," he said.
The Pope responded by saying he came as "a friend of the US".
He praised Americans for their "concern for the greater human family" and hoped this would "continue to find expression in support for the patient efforts of international diplomacy to resolve conflicts".
15 Apr: Arrives at Andrews Air Force Base
16 Apr: White House luncheon; talks with Mr Bush. Meeting with US bishops and prayer service in Washington (evening)
17 Apr: Washington Mass; addresses Catholic University; interfaith meeting
The Pope added: "I am confident that the American people will find in their religious beliefs a precious source of insight and an inspiration to pursue reasoned, responsible and respectful dialogue in the effort to build a more humane and free society."
He concluded: "God bless America".
BBC Rome correspondent David Willey, who is travelling with the pontiff, said Pope Benedict studiously avoided any direct reference to the war in Iraq or to the current campaign to elect a successor to President Bush.
He did however, our correspondent says, make an oblique reference to the tragic sacrifice of human lives caused by past conflicts and by implication, as a result of the current war in Iraq.
The topic was discussed in the private talks, the White House said, with the leaders expressing concern about the plight of Iraq's Christian minority.
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