Two churches were set on fire in the West Bank, raising to at least seven the number of church attacks in Palestinian areas over the weekend blamed on outrage sparked by the speech.
There was also concern that anger at the speech was behind the shooting of an Italian missionary nun at the hospital where she had worked for years in Somalia. The killing came just hours after a Somali cleric condemned the pope's speech.
Federico Lombardi, the Vatican spokesman, said the Vatican was "following with concern the consequences of this wave of hate, hoping that it does not lead to grave consequences for the church in the world".
Police across Italy were ordered to step up security out of concern that the anger could cause Roman Catholic sites to become terrorist targets. Police outside the pope's summer palace confiscated metal-tipped umbrellas and liquids.
The head of the Muslim Brotherhood in Egypt, a banned group but still the largest Islamic movement in that country, said the outrage was justified but predicted it would subside quickly.
Mohammed Mahdi Akef said: "Our relations with Christians should remain good, civilised and co-operative."
Germany's Central Council of Muslims welcomed the pope's comments as "the most important step to calm the protest" and urged the Vatican to seek discussion with Muslim representatives to avoid lasting damage.
But others were still demanding an apology for the words, including in Turkey, where questions have been raised about whether Benedict should go ahead with a visit scheduled for November as the first trip of his papacy to a Muslim nation.
Mehmet Aydin, the Turkish state minister, said: "It is very saddening. The Islamic world is expecting an explanation from the pope himself.
"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?"
Mohammad al-Nujemi, a professor at the Institute of Judicial and Islamic Studies in Riyadh, Saudi Arabia, expressed dismay at what he called Benedict "evading apology".
He told Al-Arabiya television: "His statements might give terrorists and al-Qaeda followers legitimacy that there is really an attempt to hurt Muslims."
"Calm and dialogue"
In Damascus, Mohammad Habash, a Syrian politician, said the pope offered a "clarification and not [an] apology". But he also called for "calm and dialogue".
Hundreds of Iranians demonstrated against the pope in cities across Iran. In Qom, the religious capital of Iran's 70 million Shia Muslims, Ahmad Khatami, a prominent cleric, said the pope and George Bush were "united in order to repeat the Crusades".
Vladimir Putin, the Russian president, earlier urged world religious leaders to show "responsibility and restraint" to avoid what he called "extremes" in relations between faiths.