(CNN) -- Muslims around the world woke up Sunday and welcomed the end of a long month of fasting with hearty greetings of "Eid Mubarak," or happy festivities.



Egyptian women perform the Eid al-Fitr dawn prayer at a stadium in Mansura, 120 km north of Cairo.



The faithful were ushering in Eid al-Fitr -- three days of celebrations that Muslims mark with joyous community prayers, acts of charity, visits from far-flung relatives, gift-giving and elaborate feasts.



"Think Christmas, Thanksgiving, New Year's -- all rolled into one. It's that huge for us," said Sajjad Aziz of Hoboken, New Jersey.



Islam follows a lunar calendar, and the timing of Eid al-Fitr varies around the world depending on when the crescent of a new moon is sighted.



So, while most countries -- including the United States -- observed Eid on Sunday, some will begin their celebrations on Monday.



The night before Eid, entire communities gather on rooftops, scanning the sky with giddy anticipation.



"It only needs one sighting of the moon in the whole country, and the whole nation erupts in cheers," said Qazi Arif, 35, of Sirajgong, Bangladesh. "It's a divine feeling, hard to describe."



Eid al-Fitr bids goodbye to Ramadan -- a month of dawn-to-dusk abstinence from food, drinks and other sensual pleasures. Muslims believe the Quran, the religion's holy book, was revealed to Prophet Muhammad during Ramadan more than 1,400 years ago.



The Eid is one of two major holidays in Islam, alongside another called Eid al-Adha. The latter commemorates the prophet Abraham's willingness to sacrifice his son, Ishmael, for God.



On the morning of Eid, Muslims don new clothes and head to prayers that are often held in open fields to accommodate crowds too big to contain in mosques.



Those who can afford it donate a small percentage of their possession or its equivalent to the poor and needy so they too can avail themselves for the celebrations. Feasts await at every house.



"It's a festival principally about community. We're even asked to take a different route when we walk back from prayers so that we can meet different sets of people to greet and celebrate with," said Wasim Iqbal of Karachi, Pakistan.



For Muslims in North America -- and countries where they are the minority -- Eid is a more subdued affair.



"If you have family close by, then you can kind of capture the mood that you remember from back home," said Abdallah Gamal, a native of Egypt who lives in St. Louis, Missouri. "But it's not the same."



Because the U.S. Census does not ask about religious affiliation, it is difficult to gauge the Muslim population in the United States. The Pew Muslim American study conducted two years ago estimated it at 2.5 million, while the Council on American-Islamic Relations places it as high as 6 million.



On Saturday, both President Barack Obama and Secretary of State Hillary Rodham Clinton offered greetings to American Muslims.



"We know there is more than unites peoples of faith than divides us," Clinton said. "So as Ramadan draws to a close, let us hold on to that spirit of community throughout the year to achieve our common goals of peace, prosperity and stability."



It is a message that Afghanistan's president, Hamid Karzai, also shared during Eid prayers when he called on the Taliban to join the peace process in his war-weary country.



The day wasn't one of universal comity, however.



In Yemen, the government and rebels accused each other Saturday of breaking a cease-fire they both asked for to commemorate Eid.



And Iran's Supreme Leader Ayatollah Khamenei used his Eid sermon to launch another volley at the country's arch-rival Israel and at Western powers.



"We're not quite there, I'll will admit," said Mehreen Ali of Boston, Massachusetts. "But have you seen an Eid prayer? Rows and
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