In the Middle East it was also time for politicians and mosque preachers to deliver political messages — some this year touching on the U.S.-led occupation of Iraq.
The three-day holiday that ends the holy month of Ramadan — Eid al-Fitr means the festival of breaking the fast — began Monday in some Muslim countries. But in most, it started Tuesday with early morning prayers in mosques and visits to cemeteries where the Quran, Islam's holy book, is read at the graves of relatives.
The start of Islamic holidays depends on sighting the new moon, and there is always confusion about when Ramadan and Eid al-Fitr begin. In Iran, only one of the four supreme Shiite Muslim clerics reported seeing the new moon, so the holiday began Tuesday in his city of Qum but was not expected until Wednesday in much of the rest of the country.
In Cairo, thousands stood in the streets around the central Mustafa Mahmoud mosque after early morning prayers. The day is traditionally a time for greeting friends, and many people — with prayer rugs under their arms or thrown over their shoulders — shook hands and exchanged embraces.
Lebanon's the top Shiite Muslim cleric, Grand Ayatollah Mohammed Hussein Fadlallah, accused the United States of employing "an imperialist mentality" in its occupation of Iraq.
"America has failed in convincing Iraqis of its good intentions … or in building a relationship with the Iraqi people away from control and hegemony," he said in a sermon at the Hasanein Mosque south of Beirut.
Palestinian leader Yasser Arafat, who has been confined to the West Bank town of Ramallah for nearly two years, said after Eid prayers that the Palestinians remain committed to the so-called road map to peace backed by the United States, United Nations and the Europeans, but accused Israel of not cooperating. "Unfortunately," he said, "the other side did not agree to the road map."
In Mecca, the birthplace of prophet Mohammed and the holiest place in Islam, Saudi King Fahd said prayers with Lebanese President Rafik Hariri at the Al Haram Grand Mosque.
Sheik Saleh bin Abdullah bin Hamid, imam of the mosque and speaker of the Shura Council that advises the king, said in his sermon that Jihad — which Muslim radicals define as holy war — should be a personal quest to dispel the wrongs being said about Islam, to show its true face.
"Islamic writers, clerics, politicians and intellectuals must work hard toward this end," he said.
Turkish Prime Minister Recep Tayyip Erdogan — whose country has seen dozens killed in four major suicide bombings in the last two weeks — delivered another type of message on the war on terrorism in a televised national address on the eve of the religious holiday.
"This is a war between justice and cruelty, good and bad, and true and false. It is our right to expect every sensible person to stand by justice, good, and truth in this war," Erdogan said.
In Iraq, where Saddam Hussein's Ministry of Endowments and Religious Affairs used to decide when Eid al-Fitr would begin, no religious authority existed to set the date this year. For Iraq's Sunni Muslims, the festival began Monday. Some Shiites celebrated it Tuesday. Others will wait until Wednesday.
Afghan President Hamid Karzai celebrated by saying he hopes Afghanistan will one day be freed from terrorism and poverty. Karzai also used his brief speech after prayers in the mosque at the presidential palace with former King Mohammad Zaher Shah, Cabinet ministers, military officials and other invited guests to call for unity, prosperity and stability among Muslims around the world.
"I pray to the Almighty that Afghanistan will escape from anger, poverty, natural disasters and terrorism, and eventually become a united country," he said.
Also on the Asian subcontinent, the Indian and Pakistani armies said they would stop firing across their international border, including in disputed Kashmir, at midnight Tuesday, the start of the festival.
In a statement, President Bush sent good wishes to Muslims.
"Islam is a religion that inspires its followers to lead lives based on justice, compassion, and personal responsibility," Mr. Bush said. "During this joyful season, I encourage people of all faiths to reflect on our shared values: love of family, gratitude to God, a commitment to religious freedom, and respect for the diversity that adds to our Nation's strength."
"Laura joins me in sending our best wishes for a joyous celebration," the president said, signing his statement "Eid mubarek," or Happy Eid.