The Roman Catholic pope is due to give his regular blessing at his summer residence Castelgandolfo on Sunday.
The Vatican issued a statement on Saturday saying the pope hoped Muslims would understand the "true sense" of the words he used in a speech at the University of Regensburg in Germany on Tuesday.
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.
Egypt's Muslim Brotherhood, however, said the pope's apology did not go far enough.
"Has he presented a personal apology for statements by which he clearly is convinced? No"
"We want a personal apology. We feel that he has committed a grave error against us and that this mistake will only be removed through a personal apology," Mohammed Habib, the deputy leader of the organisation, said.
"Has he presented a personal apology for statements by which he clearly is convinced? No," he said.
On Saturday, Morocco recalled its ambassador to the Vatican.
The pope had quoted from a medieval text which said: "Show me just what [Prophet] Muhammad brought that was new, and there you will find things only evil and inhuman, such as his command to spread by the sword the faith he preached."
The comments sparked protests from the Muslim community in the Palestinian territories, Pakistan, India, Egypt and elsewhere.
Strong protests followed the
pope's anti-Islam remarks
On Friday, thousands marched in the Gaza Strip, waving the green flags of Hamas and chanting praises to "God and his prophet".
Ismail Haniya, the Palestinian prime minister, criticised the pope's comments, saying: "These remarks go against the truth and touch the heart of our faith."
Two churches in the West Bank and several Christian institutions in Gaza were bombed, causing damage but no casualties.
Leading politicians and several prominent Christian and Muslim leaders also criticised the remarks.
Recep Tayyip Erdogan, the Turkish prime minister, called on Saturday for the pope to apologise for his "unfortunate, ugly" remarks on Islam.
The Iraqi government called for calm after a church in Basra was reportedly attacked.
Sheikh Abubukar Hassan Malin, a religious leader linked to Somalia's powerful Islamic Courts Group, called for Muslims to hunt down and kill the pope for his remarks.
"We call on all Islamic communities across the world to take revenge on the baseless critic called the pope," he was quoted by the AFP news agency as saying.
The full prepared text of the pope's speech at the University of Regensburg can be seen here