Pope Benedict XVI has apologised in person for causing offence to Muslims in a speech in Bavaria last week.
The Pope said he wanted to clarify the true meaning of his address
He said the medieval text which he quoted did not express in any way his personal opinion, adding the speech was an invitation to respectful dialogue.
Some Muslim leaders said his statement was sufficient to defuse the row, but others said it did not go far enough.
The 14th Century Christian emperor's quote said the Prophet Muhammad brought the world only evil and inhuman things.
The Pope has been under intense scrutiny amid angry reactions from throughout the Muslim world.
Reaction was mixed in Turkey, although Foreign Minister Abdullah Gul said the Pope's planned visit to the mainly Muslim country was still expected to go ahead in November.
Turkey's most senior Muslim religious figure, Ali Bardakoglu, welcomed the Pope's statement, and described his respect for Islam as a "civilised position".
But State Minister Mehmet Aydin said the pontiff appeared to be saying he was sorry for the outrage but not necessarily the remarks themselves.
"You either have to say this 'I'm sorry' in a proper way or not say it at all - are you sorry for saying such a thing or because of its consequences?" he said.
The Egyptian opposition group, the Muslim Brotherhood, welcomed what it called the Pope's "retraction", but later warned that it did not amount to a definitive apology and would not be enough to satisfy all Muslims.
In Germany, the Central Council of Muslims said the Pope had taken an important step towards calming the unrest of the past few days.
Pope Benedict XVI issued his apology from the balcony at his residence at Castel Gandolfo outside Rome as gave the Angelus blessing.
"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 told pilgrims.
"These in fact were a quotation from a medieval text, which do not in any way express my personal thought.
Several West Bank churches have been attacked
"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."
Hours before the Pope spoke, two churches in the West Bank were attacked with firebombs in what was believed to be a reaction to the Bavaria speech.
In the Somali capital Mogadishu, an Italian nun was shot dead by gunmen. The shooting may have been connected to strong criticism of the speech by a radical Somali cleric.
And in Iran, hundreds of people gathered at rallies in major cities.
Conservative cleric Ahmad Khatami compared the pontiff to US President George W Bush, saying the two were "united in order to repeat the Crusades".
In his speech at Regensburg University on Tuesday, the German-born Pope quoted Emperor Manuel II Paleologos of the Orthodox Christian Byzantine Empire.
Stressing that they were not his own words, he quoted the emperor saying: "Show me just what 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."
He also said violence was "incompatible with the nature of God and the nature of the soul".
Reactions to the speech came from such leaders as Pakistani President Pervez Musharraf, who said efforts to link Islam and terrorism should be clearly opposed.
Street protests were held in Pakistan, India, Turkey and Gaza.