The Vatican says it will contact several Muslim countries to clarify the pope's position on Islam.
In an interview with the Italian newspaper Corriere della Sera, Cardinal Tarcisio Bertone, the pope's diplomatic adviser, said the Holy See would attempt to explain the full meaning of the pope's speech to political and religious authorities in Muslim countries.
Bertone said Vatican ambassadors, or papal nuncios, would highlight passages of the lengthy speech which would help to clarify its true meaning, but which had been ignored in the furore.
At the end of a two-day visit to Venezuela, Iran's president Mahmoud Ahmadinejad said on Monday that he respected Benedict, apparently downplaying the pontiff's remarks.
"Regarding the issue of the pope's comments, we respect the pope and all of those who are interested in peace and justice," Ahmadinejad said.
On Monday, Ayatollah Ali Khamenei, the country's supreme leader, had said that the comments were part of what he called a "crusade" against Muslims.
After a meeting with George Bush, the US president, in New York late on Monday, Abdullah Ahmad Badawi, Malaysia's prime minister, was quoted as saying that the pope's expression of regret was acceptable, but that the pontiff should avoid making future comments that could offend Muslims.
"I think we can accept it and we hope there are no more statements that can anger the Muslims," Badawi said.
Malaysia, which chairs the 57-member Organisation of the Islamic Conference, previously demanded that the pope offer a full apology and retract what he had said.
Bush told the Malaysian leader that he believed the pontiff was sincere in his apology.
The head of Australia's Catholic Church welcomed the muted Australian reaction to the pontiff's comments on Islam, but said violence elsewhere in the world "justified one of Pope Benedict's main fears".
Cardinal George Pell, the leader of Australia's 5.1 million Roman Catholics, said: "The violent reaction in many parts of the Islamic world justified one of pope Benedict's main fears.
"They showed the link for many Islamists between religion and violence, their refusal to respond to criticism with rational arguments but only with demonstrations, threats and actual violence."
Australian Muslim leaders said the comments by both Benedict and Pell should be condemned.
Ameer Ali, head of a government-appointed Muslim reference group, said: "His [Pell's] comments are especially unhelpful in a charged atmosphere."