Like their fellow believers throughout the world, Washington are Muslims took the day off from work yesterday to celebrate the Feast of Sacrifice, one of the holiest festivals in the Islamic calender.

Liberian deplomats in elaborately embroidered robes, Pakistani women in gold-threaded saris and jeweled nose rings and Arab men in white burnooses thronged the Islamic Center for the traditional prayers of Eid-ul-adha, as the holiday is known.

"It's just like Christmas and Easter," explained Dr. Abdul S. Hashim, a Bethesda pediatrician, between embracing friends who thronged the outer court of the center after the prayers. "You see people once a year."

In the Islamic calender, yesterday's holiday marks the end of the pilgrimage of the faithful to Mecca, the journey every devout Muslim hopes to make during his lifetime.

The roots of the celebration go back to the prophet Abraham, who, according to Islamic tradition, demonstrated his faithfulness and obedience to his god by preparing to sacrifice his first-born son, Islamael. But at the last minute, an angel appeared and provided a sheep for the sacrifice, and Ishamael was spared.

Strictly observant Muslims today still mark the festival by the slaughter of a sheep - or more likely by arranging for a sympathetic slaughter house to do it for them - and distributing part of the meat to the needy.

"You are supposed to give a third of it to your friends, keep a third of it, and give a third to the poor," explained Leona Mahallati, a New Jersey-born nurse who converted to Islam after her marriage to an Iranian doctor. The couple and their four children live in Montgomery Country.

At the Islamic Center yesterday, site of the largest gathering of Muslims in this area, barefoot worshipers wedged into every corner of the center's turquoise and gold mosque, their shoes piled in the doorway. In accordance with tradition, women knelt on the right for the prayers of thanksgiving and the men on the left side of the floor, which was convered with carpets donated by the shah of Iran.

A classroom and two plastic-walled tents also were filled to overflowing. Some latecomers put down their prayer rugs on the rain-soaked lawn. A large basement room accommodated women with children too small to sit quietly through the prayers.

The service here began only minutes after Egyptian President Anwar Sadat's return from his precedent-shattering visit to Israel. But Dr. Muhammed Abdul Rauf, the Islamic Center's director, said he would not mentioned the events of the weekened in his brief sermon. "We try to avoid politics because we serve all nationalities," he explained.

Nevertheless, on an outside wall of the center was a poster of the Organization of Arab Students, caricaturing Sadat with a Moishe Dayan-style eye patch and advertising a protest demonstration at Egyptian Embassy.

Most of the worshipers chose to linger at the center, greeting friends with embraces and exclamations of "Eid Mobarak!" - the traditional salutation of good wishes for the holiday.

For the rest of the day, Rauf explained, they would visit in one another's homes, sharing the feasts that had been prepared.