The appeal came as the Vatican launched a diplomatic campaign in Muslim countries to quell rising anger over his remarks linking Islam with violence.
"The pope has already issued an apology and I think his views on this need to be judged against his entire record, where he has spoken very positively about dialogue," said Dr Rowan Williams, the Church of England’s senior cleric.
Tarcisio Bertone, the Cardinal Secretary of State and the pope’s top diplomatic advisor, said that Vatican ambassadors had been asked to explain the full text of the pope’s speech to political and religious authorities in Muslim countries.
The 79-year-old pontiff held talks with Roman Catholic bishops from Chad, his first meeting with clergy from a largely Muslim country since the row erupted last week.
The pontiff's comments in a speech in Germany last week, in which he spoke of a link between Islam and violence when quoting a 14th century Byzantine emperor, have caused outrage in the Muslim world.
"There are elements in Islam that can be used to justify violence, just as there are in Christianity and Judaism"
Dr Rowan Williams, Archbishop of Canterbury
Pope Benedict issued an apology for the remarks on Sunday, saying he was "deeply sorry" for any offence caused. He also stressed they did not reflect his personal opinion.
Dr Williams, stressed all religions could be misread by those seeking to justify violent acts.
"There are elements in Islam that can be used to justify violence, just as there are in Christianity and Judaism," he said.
"These religious faiths, because they are held by human beings who are very fallible, can be distorted in these ways and we all need to recognise that," he added.
Some Muslim groups have welcomed the papal apology. Mohammed Habib, a senior member of Egypt's opposition Muslim Brotherhood, told AFP they considered the apology a retraction of the pope's statement.
In India, the powerful All India Muslim Personal Law Board, based in the northern city of Lucknow, called for an end to protests against the Vatican.
However, Muslim anger is likely to remain among some followers after calls by an Egyptian-born Islamic scholar for Muslims to hold a "day of peaceful anger" on Friday to protest against the pope’s remarks.
Yusuf al-Qaradawi, a Sunni Muslim, said on Al-Jazeera that he believed the pope had "not apologised" on Sunday.
He said this Friday should involve "demonstrations or sit-ins in the large mosques in the hour following the prayers."
The head of the Islamic Association of China said Benedict had "gravely hurt" their feelings of Muslims, who would voice their "anger and condemnation".
"In his speech, Benedict had insulted both Islam and the Prophet Muhammad," Chen Guangyuan was quoted by the Xinhua news agency as saying on Monday.
Jacques Chirac, the French president, for his part warned against "anything that increases tensions between peoples or religions" in an interview on Europe 1 radio.
"We must avoid any confusion between Islam, which is, of course, a respected and respectable religion, and radical Islamism which is a totally different form of behaviour and which is of a political nature," he said.
The pope’s offending speech explored the historical and philosophical differences between Islam and Christianity, and the relationship between violence and faith.
His reference to a 14th century assessment of the Prophet Mohammed in which a Byzantine Christian emperor described the influence of Islam's founder as "evil and inhuman" triggered the current crisis.