Muslims around the world are celebrating Eid al-Fitr, a three-day holiday that marks the end of the holy month of Ramadan.

Observers of Islam in Egypt, Syria and several other Arab countries started marking the holiday Tuesday by crowding into mosques for prayers. Muslims in several non-Arab countries including Russia, Turkey and Afghanistan also began Eid celebrations Tuesday.

However, in Indonesia, the world's largest Muslim majority country, religious authorities announced that Eid will fall on Wednesday. The Ministry of Religious Affairs in Jakarta said the decision was made after consultations with astronomers, Muslim scholars and other experts who determined that Eid al-Fitr will fall on August 31.

The decision affects the celebration plans for millions of people.

The South Asian nations of Pakistan, India and Bangladesh also will mark Eid on Wednesday.

Eid al-Fitr celebrates the purification achieved during Ramadan — a month of sunrise-to-sunset fasting, one of the five pillars of Islam.

Eid is the first day of the Islamic month of Shawwal and a major holiday.

U.S. President Barack Obama has sent Eid greetings to the Muslim world. In a Tuesday statement, he said many Muslims had observed the month of Ramadan while “courageously persevering” in efforts to get “fundamental freedoms.”

Religious authorities in Saudi Arabia, home to Islam's holiest sites, started the celebrations in their country Monday. They said the new moon had been sighted and proclaimed that Ramadan ended Monday, with the Eid feast to begin the next day.

In Libya, rebel fighters ended Ramadan late Monday by resting on the road to Sirte, leader Moammar Gadhafi's hometown and one of the last bastions of his loyalist forces. The first Eid to be celebrated after Mr. Gadhafi's fall will be marked by shortages of food, water and electricity. But many Libyans say this year's holiday is priceless because they will enjoy it in freedom.