VATICAN CITY — Pope Benedict XVI said yesterday that he did not mean to malign Islam when he quoted a medieval emperor, but he did not issue the direct apology still demanded by some Islamic leaders who were offended by his remarks.

During an audience in a tightly guarded St. Peter’s Square, Benedict acknowledged that his comments — which sparked fury across the Islamic world — were open to misinterpretation.

In a September 12 address at the University of Regensburg in Germany, Benedict cited the words of a Byzantine emperor who characterized some of the teachings of the Prophet Muhammad as “evil and inhuman,” particularly “his command to spread by the sword the faith.”

“This quote unfortunately lent itself to be misunderstood,” the pope said yesterday. “For the careful reader of my text, however, it is clear that in no way did I wish to make my own the negative words of the medieval emperor.

“I wished to explain that not religion and violence, but religion and reason go together,” he added, drawing applause from the crowd of some 20,000 faithful.

Benedict repeated yesterday’s comments — originally made in Italian — in English, French, Spanish, and German, but not in Arabic.

He expressed “deep respect” for Islam and called for a dialogue among religions. “I trust that after the initial reaction, my words at the University of Regensburg can constitute an impulse and encouragement toward positive, even self-critical dialogue both among religions and between modern reason and Christian faith,” Benedict said.

Reaction was angry among Muslims worldwide. Protests took place in Indonesia, Turkey, and Syria; churches were attacked in the West Bank; an effigy of the pope was burned in Iraq; and a nun was shot dead in Somalia in an attack believed to be linked to the pope’s address in Germany.

But President Ahmadinejad of Iran — an Islamic hard-liner — said during a trip to Venezuela on Monday that he respects the pope, apparently playing down the uproar. “Regarding the issue of the pope’s comments, we respect the pope and all of those who are interested in peace and justice,” Mr. Ahmadinejad told reporters.

And Prime Minister Badawi of Malaysia said Tuesday that Benedict’s expression of regret was acceptable. Malaysia — which chairs the world’s largest Islamic bloc, the Organization of the Islamic Conference — earlier had demanded the pope offer a full apology and retraction.

The pope’s address yesterday was the second time in four days that he has sought to clarify his intentions and defuse the anger that followed his speech.

On Sunday, Benedict said he was “deeply sorry” about the reaction to his remarks, stressing that they did not reflect his own opinions. While some accepted his regrets, others said the statement did not go far enough and demanded an unequivocal apology.