From across the nation, a diverse coalition of 250,000 Americans gathered at the Lincoln Memorial yesterday to commemorate the 20th anniversary of the historic March on Washington and to rekindle Martin Luther King Jr.'s dream of equal justice and economic opportunity for all.

More than 700 groups with a wide range of political and social agendas came to Washington demanding everything from government job programs to a nuclear freeze to gay rights. But their unifying theme, aside from the march's official call for "Jobs, Peace and Freedom," was unquestionably the goal of ousting President Reagan.

"We serve you notice, Mr. Reagan, that we are not here to live in the past and leave here simply singing, 'We Shall Overcome,' " warned Benjamin Hooks, executive director of the NAACP, who led the crowd in a chant of "Reagan No More in '84." "We are here because we are committed to the elimination of Reaganism from the face of the earth. We have had enough of it."

March on Washington II, as it was billed by the organizers, who described themselves as a "New Coalition of Conscience," drew roughly the same turnout as the historic gathering on Aug. 28, 1963, called by labor, religious and black.

The 1,500 buses that came to Washington was about the same number as in 1963, and while far fewer "freedom trains" carried marchers here this time, the slack was picked up by residents of the Washington area, who police said came in numbers that surpassed 1963.

Like the 1963 gathering, the event was peaceful and relatively problem-free considering the immense logistical tasks of gathering, moving and tending to the needs of a sweltering multitude throughout an 11-hour program that did not end until after 7 p.m.

The day was long and hot: more than 600 marchers were treated for heat exhaustion as temperatures reached 95. The oratory, too, was often heated, as speaker after speaker tried to recreate the intensity of King's 1963 "I Have a Dream" speech that galvanized the civil rights movement.

Fifteen years after his death, King still electrified the crowd as few of yesterday's speakers could: a recorded version of his speech thrilled the crowd again as it was played on the loudspeakers toward the close of the program that ended with the joining of hands and the singing of "We Shall Overcome."

The diverse groups of marchers--black and white, old and young, representing nearly every religious group and spanning a range of political and social beliefs from communism to vegetarianism--seemed to be striving for a spiritual unity that would incorporate the past dreams of King and the current goals of their groups.

"We must dream new dreams," shouted the Rev. Jesse Jackson, head of Operation PUSH, whose often-angry speech appeared to draw the most fervent response from the crowd. "Our day has come. Don't let them break your spirit. Hold on to your dreams."

The marchers--many of whom arrived in groups after all-night bus or train rides--carried official and handmade signs and sported colorful buttons and T-shirts proclaiming their messages: "Hell is War," "Give Back the Earth," "Military Intelligence is a Contradiction in Terms," "Bread, not Bombs," "Remember: 1963-1983," "A Dream Deferred is No Dream at All," and many more.

The style of yesterday's march contrasted sharply in many ways to 1963. Many in the overwhelmingly black crowd of 20 years ago wore suits and ties and dresses, while yesterday's crowd, with a higher percentage of whites, came clad more casually, in T-shirts, shorts and sundresses that gave the occasion a more festive air.

After a morning program, during which more than 24 "feeder" marches streamed onto the Mall from neighborhoods throughout the city, the crowd spilled onto Constitution Avenue and began marching to the Lincoln Memorial. Loud chants for the proposed Equal Rights Amendment mingled with soft gospel tunes; there were marchers singing "We Shall Overcome" and then shouting, "RIF Reagan, RIF Reagan." There were expressions of anger, followed by words of love.

Among the more than 70 speakers who addressed the crowd during the day, several entertainers long associated with civil rights causes drew some of the most spirited response. Folk singer Pete Seeger rewrote the words to the classic "This Old Man" song to include a verse telling the president to go back home to California. Comedian Bill Cosby referred to Reagan as "Ronald Dancing Mouth." As the program neared its close, singer Stevie Wonder asked the crowd to hold their hands to their hearts and join him in a quest for "a united world. . . and a respectable job, absolute peace and sincere and just freedom for everyone."

Coretta Scott King, widow of the slain civil rights crusader, invoked her husband's memory during a morning address, assuring the crowd "he will be marching with us today. . . our drum major" for a new coalition. After the assembled mass marched from the monument to the memorial, she cited her late husband's opposition to the Vietnam War and stressed the relationship between domestic and foreign policy concerns: "We must demand justice in Harlem and in the Bronx. . . but also in the Philippines. We must demand justice in the barrios of Los Angeles. . . but also in El Salvador."

The repeated calls for a new political coalition stressed the importance of voting to bring about change--from the White House to the state capitals and city halls. Jackson, who has been traveling the country urging blacks to register to vote, said the Voting Rights Act, passed after the 1963 march, has since been "sabotaged," denying blacks their rights. Although poll taxes, literacy tests and violence no longer keep blacks from voting, he said, new "illegal" roadblocks have arisen in the form of gerrymandering and arbitrary voter registration practices, especially in the South.

Jackson, who is flirting with the idea of running for president and was interrupted by cries of "Run, Jesse, run," told the crowd in strident cadence, "We need not explode through riot, nor implode through drugs. We can have change through elections and not through bloody revolution. . . . We can move from racial battleground to economic common ground."

The 1984 presidential contest was a constant topic yesterday. Some of the major Democratic presidential hopefuls marched, but none spoke. Speakers and entertainers alike angrily attacked Reagan's domestic and foreign policies. Many had their own special criticisms:

"Reagan's not good enough for America," argued C.T. Vivian, head of the Anti-Klan Network, who complained the Reagan Justice Department has not done enough to fight perpetrators of racial violence.

"I don't like how he dismantled the EPA Environmental Protection Agency ," said Eleanor Seagraves, 56, a District resident who attended the march with her son, Nick, 34, and a carried bottle of water to help her through the long, blistering day.

Reagan, the subject of all this acrimony, was vacationing in Santa Barbara, Calif., yesterday but sent a message to march leaders calling the 1963 March on Washington "a noble cause." Reagan said, however, that much more still needs to be done to fulfill King's goal "of a more just, more abundant, more free society."

Organized labor--from Minnesota carpenters to Rhode Island bus drivers, from Tennessee furniture-makers to Florida postal clerks--brought a substantial contingent to the march, estimated at 50,000 to 60,000 by AFL-CIO officials.

The labor turnout, perhaps one-quarter of the total, represented a dramatic change from 1963, when the AFL-CIO refused to endorse the march.

The peace and antinuclear movements, practically nonexistent 20 years ago for most Americans, were widely represented. Numerous religious and antiwar organizations turned out. A Buddhist monk, in his 22nd day of a fast to end the nuclear arms race, was wheeled through the crowd.

Women, who were almost overlooked when it came time to preparing the program for the 1963 march, appeared to outnumber the men this time, and their concerns--and political clout--were highly visible.

"We will change the political landscape of this nation with the power of the gender gap and the women's vote," said Judy Goldsmith, president of the National Organization for Women.

Despite the diversity of issues and groups, it was still the memory of King that dominated the day. "Thanks be to God for giving us Martin Luther King Jr.," his widow declared as the long day came to an end. "And thank you Martin for being with us today. Thank you for your dream. We are so proud to celebrate this day. Your day, Martin, your day."