A woman takes a picure of children in front of the Dome of the Rock at the Al Aqsa Mosques compound on Friday. AFP

After the Ramadan month of fasting, Muslims celebrate Eid Al Fitr with feasts and family visits. The start of the holiday is traditionally based on sightings of the new moon, which vary according to geographic location.

In Jerusalem, thousands of faithful gathered at Islam's third holiest shrine, the Al Aqsa Mosque compound. Following holiday prayers, a clown entertained children and a woman painted the cheek of a girl with the green, red, black and white Palestinian flag.

The streets of Arab capitals of Damascus, Baghdad and Beirut were crowded with worshippers heading to mosques and cemeteries.

Many Muslims visit the graves of their loved ones after the early morning prayer on the first day of Eid Al Fitr. Visitors toted bouquets of flowers, jugs of water for plants, and brooms to clean gravestones.

"After the Eid prayer we always visit our dead … to pray and pay our respects, may God have mercy and forgive them on this blessed day,” said Atheer Mohamed in Baghdad’s Azamiya cemetery.

Islam's holidays follow a lunar calendar. But some countries rely on astronomical calculations rather than physical sightings. This frequently leads to disagreements between religious authorities in different countries - and sometimes in the same country — over the start date of Eid Al Fitr.

This year, Saudi Arabia and many other Arab countries began their Eid celebrations on Friday, while Iran, Pakistan and Indonesia, among others, set the first day of the holiday for Saturday.

In Afghanistan’s Kabul, where worshippers gathered under the watchful eyes of its Taliban rulers, 35-year-old Abdul Matin said, "I wish that besides security we had good income and good jobs. Unfortunately people can’t afford to buy all their necessities at this difficult time.”

In Turkey and Syria, many are still mourning loved ones lost in the devastating 7.8 magnitude earthquake that struck the two countries on Feb. 6, killing more than 50,000 people.

Turkish President Recep Tayyip Erdogan on Friday performed morning Eid prayers at Hagia Sophia, the 6th century Byzantine church in Istanbul that was turned into a mosque in the 15th century. It became a museum in 1934 and was reconverted into a mosque three years ago.

Erdogan, who is facing elections next month amid an economic crisis and the fallout of the earthquake, handed out chocolate and pastries to journalists outside the mosque, renamed Holy Ayasofya Grand Mosque.

In the United States, celebrations among the Sudanese community were tempered with concern for the homeland. They still gathered in large numbers for Friday prayers at the Muslim Community Center in Silver Spring.

"We are not in a mood to do anything joyful, but we’re doing (these celebrations) for the kids,” said Shaza Ahmed, who is among an estimated 20,000 Sudanese in Maryland and Virginia.

In Tennessee, where school state testing was underway, Imam Ossama Bahloul at the Islamic Center of Nashville said that for the first time, his daughter missed the holiday prayer with the family so she could take an exam.

In Minneapolis, Friday public school classes were called off for the first time to mark the holiday. About 10% of students are Muslim, said Jaylani Hussein, director of Council on American-Islamic Relations-Minnesota.  "In Minneapolis, you can be unapologetically Muslim,” Hussein said.

In Dearborn, Michigan, employees have Eid Al Fitr off as a paid holiday for the first time. Mayor Abdullah Hammoud said the precedent was not planned but that it was important for Muslim employees "to feel included and enjoy the holiday with their families.”

Associated Press