Cardinal Angelo Scola, of Venice, who publishes Oasis, a multilingual journal of Catholic-Muslim dialogue, spoke of Muslims as "brothers and sisters."
Tuesday's friendly gathering followed a tumultuous year in which some Muslims responded violently to a September speech by Pope Benedict XVI in Regensburg, Germany. In the speech, the pope quoted a medieval Byzantine emperor who had said that Islam's only innovation was to spread faith by violence.
The point of the pope's speech was to stress the need for faith to apply reason and to criticize some Christian efforts to unhinge faith from reason.
In the ensuing furor -- including church bombings and the murder of a nun in Somalia -- the pope repeatedly said the quote did not reflect his own view. But it was not until two months later, when he prayed silently alongside an imam in an important mosque in Turkey, that tensions eased.
Today questions remain about relations between the Catholic Church and the world of Islam. Even before the speech in Regensburg, some analysts believed Pope Benedict intended to take a harder line with Islamic leaders than had Pope John Paul II, especially in insisting that churches in predominantly Muslim lands have the same rights that mosques have in Rome. A few later theorized that the offending quotation was a deliberate provocation intended to prove the emperor's point.
But the latter theory conflicts with the pope's own language about Islam.
Three months after his 2005 election, when young Muslims bombed the London subway, the pope refused to endorse the idea that the violence stemmed from inevitable conflict between Islam and the West. "Terrorism is not a clash of civilizations, but the action of groups of fanatics," he told journalists.
Six months before the Regensburg speech, he told American Jewish leaders that "Judaism, Christianity and Islam believe in the one God, Creator of heaven and earth. It follows therefore, that all three monotheistic religions are called to cooperate with one another for the common good of humanity, serving the cause of justice and peace in the world."
The enormous publicity given the post-Regensburg furor drowned the voices of many Muslims and Catholics who are working for better relations.
Among them is Cardinal Scola, 65, who was on the lists of likely successors to Pope John Paul and is young enough to be considered again at the next conclave. Unpretentious, affable and fluent in English, he is a strong advocate of church teaching on abortion, bioethics and marriage. He is no relativist, and is clear about Christianity's theological differences with Islam. But he warns against demonizing Muslims.
In an interview on Tuesday with the conservative Catholic cable network EWTN, he drew a firm distinction between Islam and a militant ideology that distorts it for political ends. He called the ideology that fuels terrorism "a parasite" on Islam.
"Violence is not coming from the religion, but from the ... ideology that has entered into the religion," Cardinal Scola said. "Don't attribute to the religion what we must attribute to the ideology."
He encouraged Catholics to engage in their own friendship-based dialogue with Muslim neighbors and co-workers, testifying through good behavior as well as words. And he urged Christians in America to learn from Christian minorities in predominantly Muslim countries about how to engage with Muslims.
It is necessary to press for religious freedom in countries that lack it, the cardinal said. But Christians must provide models of this freedom by granting it fully and cheerfully to religious minorities themselves.
The problem of religious freedom in Islamic countries will not be solved overnight, he said.
"It is a long process, the process of listening," he said. "We have to move step by step with courage, but also with patience."
With a small group of Catholic and Islamic scholars and others, he spent the afternoon in private dialogue with India-born Dr. Muzammil Siddiqi an influential Islamic leader in Southern California. He was chairman of the Fiqh (Islamic Law) Council of North America in 2005 when it issued a ruling -- later endorsed by 100 Islamic groups -- that all terrorist violence violates Islam.
The purpose of interreligious dialogue, Dr. Siddiqi said, "is to clear the world community of prejudice. ... It is to live together in the global village in harmony, peace and recognizing the rights of others."
He acknowledged that Christians and Muslims have very different views of God's nature and the identity and mission of Jesus, but said he preferred not to stress the "uniqueness" of each faith.
"The basic purpose of Christianity and the basic purpose of Islam is to make better human beings," he said.
Inamul Haq, a Muslim who teaches at the Catholic Theological Union -- a Chicago seminary -- was optimistic about the future, despite last year's setbacks.
"Pope John Paul II showed much more openness and a welcoming attitude toward Muslims. But I think that in the long run his legacy will survive and grow and flourish," said Dr. Haq, who surveys shared themes in Judaism, Christianity and Islam.
He doesn't believe Pope Benedict intended to insult Islam at Regensburg, calling it "a slip."
"He made more than one apology ... . And after the incident, there has been greater activity on the part of Muslims and Catholics to understand each other."
Much of that activity has occurred on a local, grass-roots level, he said.
The Tampa chapter of the Council on American-Islamic Relations, for example, raised money to repair six West Bank churches that were fire-bombed after the pope's speech.
"While we were upset about the pope's comments, we were more upset that individuals who may claim to be Muslim would use violence to try to respond to the pope's remarks," said Ahmed Bedier, executive director of CAIR's Tampa chapter.
"We were helping those churches, but also helping to heal those Catholic-Muslim tensions that existed," Mr. Bedier said.
None of the damaged churches was Catholic. But a papal charity, the Catholic Near East Welfare Association, agreed to get the money to the churches, regardless of denomination.
The gift was publicized in Florida but not nationally, even as stories of Muslims attacking Catholics overseas continued.
"I think it's unfortunate that people don't always see the good things that Muslims do," Mr. Bedier said. "But local people saw it in action. And it moved people's hearts here."
At the Pope John Paul center last week, a Franciscan friar wept as he spoke of the evening's discussion.
"Certainly the word we heard so many times tonight that pulls us together as a glue is 'hope,' " said the Rev. Edward Ondrako, who teaches theology at the Catholic University of America.
Father Ondrako spoke of a Muslim man, educated at Catholic schools in Egypt, who sat next to him Tuesday. He came from Brooklyn to bear witness of his love for Catholics.
"If you multiply that man a million times in both the Catholic world and the Islamic world, you will have a real igniting of love," Father Ondrako said.