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On an highly emotional spiritual level there has been a great common-ground meeting place between Rome and Mecca in the town of Fatima in Portugal. To quote a Catholic news organization, "Our Lady of Fatima is really Fatima, daughter of the Prophet Mohammed." On October 23, 1995, Iranian television began running stories that the apparitions in Fatima, Portugal in 1917 were religious phenomena of Muslim origin....
....According to Iranian Television, the woman who appeared to the three shepherd children in 1917 was not the Virgin Mary, mother of Jesus, but Fatima, the daughter of the prophet Mohammed, founder of Islam. Her message was reported to be "I am Fatima, daughter of the Prophet of Islam." This television report has helped launch the growing waves of Muslim pilgrims who have been visiting this Christian site in Portugal in recent years.
Catholics, on the other hand, say that the Blessed Virgin Mary appeared to the three shepherd children. She told them to pray, especially encouraging the prayer of the Rosary. Lucía, the only surviving recipient of the vision, was entrusted with three "secrets," of which the third has never been made public. She recently assured that the third secret was never intended for general proclamation. Pope John Paul II has had a strong devotion to Our Lady of Fatima, especially since the failed assassination attempt of Ali Agca, which occurred precisely on May 13, 1991, the anniversary of the first vision at Fatima (May 13, 1917).
-- From the thread The Papacy and Islam

This brings us to our second point: namely, why the Blessed Mother, in the 20th century should have revealed herself in the significant little village of Fatima, so that to all future generations she would be known as "Our Lady of Fatima." Since nothing ever happens out of Heaven except with a finesse of all details, I believe that the Blessed Virgin chose to be known as "Our Lady of Fatima" as a pledge and a sign of hope to the Moslem people, and as an assurance that they, who show her so much respect, will one day accept her divine Son too.
Evidence to support these views is found in the historical fact that the Moslems occupied Portugal for centuries. At the time when they were finally driven out, the last Moslem chief had a beautiful daughter by the name of Fatima. A Catholic boy fell in love with her, and for him she not only stayed behind when the Moslems left, but even embraced the Faith. The young husband was so much in love with her that he changed the name of the town where he lived to Fatima. Thus, the very place where our Lady appeared in 1917 bears a historical connection to Fatima, the daughter of Mohammed.
-- Archbishop Fulton Sheen, in the book The World's First Love

On the Lady of Fatima:
Our Lady of Fatima in the Light of History
The Papacy and Islam
Mary And The Moslems(The Virgin Mother Mary & Islam)
Area Catholics to celebrate 90th anniversary of Fatima
New movie about Our Lady of Fatima to be screened in major U.S. cities
Fatima: The new Movie… Deception a-go-go [the Fatima apparitions were really UFO manifestations]
On Catholics joining hands with Muslims:
Malaysia Catholics oppose non-'Allah' Bible
Catholic church in Cologne collects money for a mosque
A Catholic Church (in Venice Italy) Turns Into A Mosque (each Friday)
Muslims seek crisis management plan with Vatican
Pope meets with Muslim scholars, urges better ties
Vatican, Muslims prepare historic meeting with Pope
Muslim-Catholic pact to foster respect
Pope offers 'working meeting' with Muslims
Why Benedict XVI Is So Cautious with the Letter of the 138 Muslims
Muslims and Catholics release mission statement
Muslims, Catholics find common ground
Muslims Get "Prayer Room" at Catholic University
New York Catholics visit mosque, learn about Islam
Catholics Ponder Muslim Coexistence
Pope Invites Muslims to Dialogue, Slams "Holy Wars"(Hooray for the Pope!)

From the Catechism of the Catholic Church:

841 The Church's relationship with the Muslims. "The plan of salvation also includes those who acknowledge the Creator, in the first place amongst whom are the Muslims; these profess to hold the faith of Abraham, and together with us they adore the one, merciful God, mankind's judge on the last day."