President and Mrs. Reagan, Vice President and Mrs. Bush and scores of congressional leaders and diplomats gathered with ordinary Washingtonians under the soaring arches of Washington Cathedral yesterday for a brief, heartfelt tribute to slain Egyptian President Anwar Sadat.

The interdenominational service, intended to honor Sadat's contributions to peace and to mourn his passing, lasted barely a half hour as representives of Islamic, Jewish, Catholic and Episcopal faiths offered scriptures and prayers to Sadat's memory. But there was one moment that was electrifying:

It came when Shaik Fathy Mady, a Koranic reader, lifted his pure tenor voice in sinuous, coiling song, chanting verses of the Islamic holy scriptures that recalled Sadat's devout Moslem beliefs and evoked his homeland. For five minutes the voice soared, his pauses finding total silence.

When he finished, the large Egyptian delegation, led by Ambassador Ashraf Ghorbal, seemed transfixed; several women dabbed their eyes.

"The world has lost . . . one of its brightest lights of hope for the future of this planet," said the Rev. John T. Walker, Episcopal bishop of Washington, in his eulogy of Sadat.

"None of us will ever forget the faith and courage of this man," Walker said. Sadat, through his peace initiatives with Israel, taught the world that "enmity, the barrier that divides us from one another, is not a natural element of the earth. He helped to show us that enmity is something that we grow inside ourselves," he said.

Bush and his wife Barbara arrived ahead of the president with Secretary of State Alexander M. Haig. They took seats to the side in the cathedral's North Transcept. Just before the service, Bush crossed the wide aisle to greet Ghorbal and to offer condolences.

Then, just as the 4 p.m. service was about to begin, the Reagans arrived and sat quietly in the front row.

A bus brought congressional dignitaries, including Sens. Charles Percy, Charles McC. Mathias and John Glenn, from Capitol Hill to the cathedral that sits atop Mount St. Alban. Effi Barry, wife of Mayor Marion Barry, was also present, as were a host of diplomats and scores of area residents, most of whom had learned of the service via radio and television broadcasts. Several hundred persons attended the ceremony.

The Rev. Charles A. Perry, provost of the cathedral, opened the service with the quotation from Isaiah that Sadat had used at the White House ceremony when he and Israel's Prime Minister Menachem Begin signed the Camp David peace accords: "Then they shall beat their swords into plowshares, and their spears into pruning hooks."

A choir sang the 23rd Psalm, accompanied by the massive pipe organ whose lowest tones were felt rather than heard. Rabbi Eugene J. Lippman of Temple Sinai read from the Old Testament, and the Rev. Eugene A. Marino, auxiliary bishop of the archdiocese of Washington, read from the New Testament.

Walker said the officials who came to the cathedral represented all Americans in their tribute to a man who came to enjoy wide popularity in the United States.

He said that Sadat's life had shown "that in the midst of death there is life, in the midst of darkness there is light, in the midst of despair there is hope," as he called on nations to forsake "oppression and terrorism."

"Into Your healing presence," Walker prayed at the close of his eulogy, "we commend this great man."