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Riyadh also sent its top diplomat to Syria to meet with President Bashar Assad on Tuesday, a significant step towards ending his political isolation and potentially returning the war-torn country to the Arab League.
However, Tehran and Riyadh disagreed on the start of he holiday - for Saudis, Eid al-Fitr would begin Friday while officials in Iran said it starts on Saturday.
The start of the holiday is traditionally based on sightings of the new moon, which vary according to geographic location, while some countries rely on astronomical calculations rather than physical sightings to determine the start of Eid al-Fitr.
United Arab Emirates and Qatar, followed Saudi Arabia and announced the holiday would begin for them on Friday, while their Gulf Arab neighbor, Oman, declared that the moon had not been sighted and the holiday would begin on Saturday.
Iraq's Sunni authorities announced the holiday would begin Friday, while the country's top Shiite cleric, Grand Ayatollah Ali al-Sistani, set a Saturday start date. The governments of Lebanon and Syria, both in the throes of crippling economic crises, said Friday would mark the beginning of the dayslong holiday.
Indonesia's Security Minister Mohammad Mahfud called on Muslims to be respectful of each other's celebrations, and asked Muhammadiyah members to have their holiday feasts at home - in consideration of the Muslims who would still be fasting on Friday.
The country's roads and highways were gridlocked as millions crammed into trains, ferries, busses and on motorcycles, as they left cities to return to their villages to celebrate with family. The government estimated that more than 123 million travelers were expected to crisscross the vast archipelago that spans 17,000 islands, with about 18 million departing from Jakarta's greater metropolitan area.
Meanwhile, clerics of Pakistan's state-backed moon sighting committee announced at a news conference in Islamabad that Eid al-Fitr would be celebrated on Saturday in Pakistan as there were no sightings of the moon there.
Egypt and Jordan said that for them, Eid al-Fitr would begin on Friday. In divided Libya, the religious authorities based in the capital of Tripoli, said it would start on Saturday. In the country's east, run by a rival administration, authorities marked Friday as the start.
In Afghanistan, the head of the Taliban-appointed judiciary, Abdul Hakim Haqqani, also said the holiday would start on Friday.