The pontiff will call for terrorists to convert to Christianity, saying: "Turn to Your way of love those whose hearts and minds are consumed with hatred.
"God of understanding, overwhelmed by the magnitude of this tragedy, we seek your light and guidance".
The prayer is likely to further incense the Muslim world, which has already attacked the Pope for publicly converting Magdi Allam, a journalist and one of Italy's most high-profile Muslims, at Easter.
Osama bin Laden accused the Pope of trying to provoke "a new crusade" against Islam.
The Pope will also ask for "eternal light and peace to all who died" in the tragedy. His prayer will remember "the heroic first-responders: our firefighters, police officers, emergency service workers… along with all the innocent men and women who were victims of this tragedy".
Around 3,000 people died in the attacks on the World Trade Centre, including the 19 hijackers. The prayer will also mention the victims "on the same day at the Pentagon and in Shanksville, Pennsylvania".
The Pope will conclude: "Bring Your peace to our violent world: peace in the hearts of all men and women and peace among the nations of the earth." He will then sprinkle the crater with holy water and bless the site.
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