Eid al-Fitr festivities marking the end of the Muslim holy fasting month of Ramadan will be celebrated from Tuesday in Saudi Arabia, Lebanon, Libya and Jordan, officials said.
Religious authorities in Saudi Arabia, home to Islam's holiest shrines, said the new moon had been sighted and that Ramadan would end on Monday with the feast to follow the next day. Lebanon and Jordan made similar announcements.
The Islamic calendar is a lunar one, and most Muslim countries set the beginning of Eid al-Fitr by the sighting of the new moon.
In Egypt, however, the feast will start on Wednesday, the mufti, or the country's highest religious authority, announced on state television.
During Ramadan, observant Muslims abstain from eating, drinking, smoking and sex between dawn and sundown each day, after which they break their fast in what is known as iftar.
The Jewish community in Israel and around the world began its celebration of Rosh Hashana, the Jewish New Year, Monday night, which lasts until Wednesday.
Millions of Jewish worshippers are expected at the Western Wall, the remains of Herod's Temple destroyed by the Romans in the year 70 AD, located in the Old City of Jerusalem.
The wall is situated on the western flank of the Temple Mount, the principle holy place in Judaism, which is also called al-Haram ash-Sharif or "Sacred Noble Sanctuary", and is the third holiest site in Islam.
Israel closed the West Bank on Sunday at midnight ahead of the celebration of Rosh Hashana, amid fear of attacks by Palestinian militants.
The West Bank is routinely closed before Jewish holidays.