Today's 20th anniversary March on Washington, expected to draw about 250,000 demonstrators, "will have its own spirit" and be as special as the historic 1963 gathering here, the widow of civil rights leader Martin Luther King Jr. said yesterday.

"This is a grass-roots movement that has suddenly caught fire," said Coretta Scott King, speaking of the diverse coalition of civil rights, peace, women's, labor, environmental, gays' and other groups that will rally on the Mall today on behalf of the march's theme of "Jobs, Peace and Freedom."

She said what marchers of all groups are "really yearning for again is to have that feeling of oneness" projected at the original march by her husband's "I Have a Dream" speech.

The march is scheduled to get under way at 10:30 a.m. from the Mall at 14th Street, with the formal program set for 1 p.m. at the Lincoln Memorial. There also will be a rally and music beginning at 8 a.m. at the premarch assembly area, and another preprogram rally at noon at the Memorial grounds.

Weather forecasters are predicting sunny, hot and humid weather, with afternoon highs reaching the low or mid-90s.

In a series of forums held yesterday, King and other prominent civil rights leaders and march organizers talked about the purposes of the march and compared its objectives--and its missteps--with those of the march 20 years ago.

"There was just as much confusion around goals" in 1963, King said.

In 1963, organizers of the original march recalled yesterday, civil rights leaders forgot until almost the last minute to include a major woman speaker. Yesterday, it was gay rights activists whom many of the key march leaders were trying to placate.

King, D.C. Del. Walter Fauntroy, Dr. Joseph Lowery, president of the Southern Christian Leadership Conference, and Judy Goldsmith, president of the National Organization for Women, appeared at a news conference with D.C. Mayor Marion Barry to reaffirm their "personal" endorsement of gay rights and gay-rights legislation and to announce that a gay-rights speaker, poet and author Audre Lorde, would be allowed to address the march rally.

Fauntroy said earlier this week that no gay- or abortion-rights speakers would be part of the program because their inclusion might be objectionable to some members of the march coalition.

The march is not officially endorsing gay-rights legislation, and Virginia Apuzzo, director of the National Gay Task Force, while hailing the agreement on a speaker as a breakthrough, said she was still disturbed that a gay-rights advocate would not be among major speakers who are being given five minutes each on the program.

Atlanta Mayor Andrew Young, addressing the National Press Club, emphasized the positive aspects of the coalition's diversity yesterday, saying it may spawn a new political movement that will become "a gigantic organizing committee for America's future."

Young, a close associate of Dr. King, said the coalition could become "a powerful organizing force" that could achieve "the desegregation of corporate America," the conversion of military spending to domestic needs, the defeat of President Reagan and the return of Democratic control in the Senate.

Recalling the 1963 march, Young said that at that time, after years of bitter and bloody desegregation battles primarily in the Deep South, "many of us were not that enthusiastic about coming to Washington. We thought it was just going to be a big picnic."

But to their surprise, he said, civil rights leaders quickly realized that the march became pivotal in transforming "what started as a southern movement against racial segregation into a national movement" for civil rights, jobs and other goals.

"We became. . . the world's largest organizing committee, a de facto steering committee for the 1960s, setting the agenda for the '60s," he said. The current march can play a similar role for the 1980s and beyond, he added.

Young said he believed the thrust of civil rights efforts in the '80s should be along the lines taken by the Rev. Jesse Jackson's Chicago-based People United to Save Humanity, which focuses on bringing blacks into entrepreneurial roles in corporations, business franchises, advertising firms and elsewhere.

The civil rights effort, however, should transcend blacks and involve all "people of good will--as Dr. King called them" who believe in a unified America, Young said.

About 15,000 out-of-town marchers are being housed and fed with the cooperation of local churches, schools, recreation centers, merchants and other institutions and private individuals, march organizers have said.

An interfaith service last night at the Metropolitan AME Church that attracted a standing-room-only crowd of about 2,000 was among several held throughout the city.

A joyous crowd there punctuated an address by Jackson with singing, handclapping and amens.

"In 1963, there was a march for freedom," Jackson said. "In 1983 we much march for equality. In 1963, we marched in, now we must march up. The poor need protection."

A smaller, more reverent crowd of about 300 gathered at the Temple Sinai at 3100 Military Rd. NW to hear King and Jewish leaders.

"Jews have supported black Americans in their quest for equality because it is morally right," King said. "It is for this same reason that responsible black Americans will continue to vigorously oppose anti-Semitism in America."

Rabbi Alexander Schindler said that "I am proud that the movement of Reform Judaism will take its place among the hundreds of thousands of Americans of every race, religion and walk of life who will be marching together for justice, peace and freedom. Our presence will be consonant with the highest moral and ethical values of the Jewish tradition. It will be in keeping with our devotion to the security and dignity of Israel and its people. . . . "

The New Jewish Agenda sponsored another service at George Washington University's Marvin Center, where Martin Luther King III was to help light the Sabbath candles.