He told pilgrims, standing in heavy rain at his Castelgandolfo summer residence near Rome on Sunday, he was shocked by the reaction to his speech given at the University of Regensburg in Germany on Tuesday.
"I am deeply sorry for the reactions in some countries to a few passages of my address at the University of Regensburg, which were considered offensive to the sensibility of Muslims," he said.
"These in fact were a quotation from a medieval text, which do not in any way express my personal thought. I hope this serves to appease hearts and to clarify the true meaning of my address, which in its totality was and is an invitation to frank and sincere dialogue, with mutual respect."
The Vatican issued a statement on Saturday saying the pope hoped Muslims would understand the "true sense" of the words he used in the speech.
The statement, issued by Cardinal Tarcisio Bertone, the Vatican secretary of state, said the pope was "extremely upset" that parts of his speech "were able to sound offensive to the sensibilities of Muslim believers".
Bertone added that the comments, which led to several protests, had been interpreted in a way "that does not at all correspond to his intentions".
"The pope is unequivocally in favour of dialogue between religions and cultures," he said.
Click here for the pope's remarks on Sunday.he full prepared text of the pope's speech at the University of Regensburg on Tuesday.
Click herefor t