The words and deeds of Martin Luther King Jr. were evoked in Washington and across the nation yesterday as thousands paid tribute to the memory of the slain civil rights leader on the anniversary of his birth 56 years ago.

King's birthday will not be a national holiday until next year, but many local jurisdictions already honor the day by closing schools and government offices. Here and elsewhere, there were prayer breakfasts, memorial ceremonies, parades, marches and promises that King's Christian-based philosophies will live on.

Reminiscent of King's challenge to segregation in America's South in the 1950s, a larger-than-usual crowd of several hundred attended the now-daily demonstration at the South African Embassy here to protest that nation's apartheid policies. Speakers, including Mayor Marion Barry, invoked King's name, and afterward, 17 persons were arrested, including Barry's wife Effi, a number of the mayor's top aides, and United Auto Workers president Owen Bieber. See related story, Page A8.

The spirit of the day may have best been captured yesterday morning, as thousands braved wintry winds along Martin Luther King Jr. Avenue in Southeast Washington to witness the city's seventh annual King parade.

Radios blared King's famous oratory and street vendors hawked anything with his face on it. Teen-agers born after King's assassination in 1968 wore King buttons next to their Prince and Michael Jackson pins.

"It was really enjoyable," Darlene Whitney, 29, said after the parade. "I remember going out to the Washington Monument every year when we were trying to get this holiday. Now we've got it."

President Reagan issued a statement yesterday calling King "a deeply respected leader of international stature who helped lead an extraordinary revolution in America's laws and customs."

In the Atlanta neighborhood where King was born, marchers took to the streets. Walking 10 abreast, they sang freedom songs, conjuring up images of King and his supporters that some only knew from decades-old news footage. King's widow, Coretta Scott King, and Atlanta Mayor Andrew Young led a memorial service at Ebenezer Baptist Church, where King and his father were ministers.

In Chicago, Mayor Harold Washington, the Rev. Jesse L. Jackson, and entertainers Stevie Wonder and Pete Seeger joined with King's youngest son, Dexter, to celebrate King's legacy.

Sen. Edward M. Kennedy (D-Mass.) spoke at a memorial service in Boston. King also was remembered at a service in Memphis, where he was killed nearly 17 years ago.

There were commemorations of King's birth all around Washington. An estimated 600 people gathered in the presidential ballroom of the Capital Hilton for the first annual King memorial breakfast. The city held an official commemoration at the Martin Luther King Jr. library, which, Barry promised, will be the site of a new $250,000 mural depicting King's life. And hundreds more spoke of King in hallowed tones from Capitol Hill offices to the Israeli Embassy, where a reception was held in King's honor.

"We heard the dream," the Rev. Lewis M. Anthony, chairman of the steering committee of the King Metropolitan Washington Support Group, said at the memorial breakfast. "We believe in the dream. . . . And we've come to give our bodies today that if we have anything to do with it, the dream will never die."

"It's been 30 years since the seamstress Rosa Parks refused to give up her seat to a white passenger," the Rev. Bernard Lee, one of King's longtime associates and now a member of Howard University's School of Divinity, said at the King Library observance. "And the dream, this morning, is hanging on and doing quite well."

Barry told the crowd of about 800 at the library that plans are being made for a new mural on the west wall inside the building to depict episodes from King's life -- from separated Atlanta to the first March on Washington. The mural, which will be 7 feet tall and 56 feet long, will be completed next year, the mayor said.

"We'll probably be the first in the country to have such a mural," he said. Barry said much of the cost would come from private donations, but added that he will propose in his 1986 city budget that "the city match dollar for dollar the citizens' contribution."

Barry also reminded the audience that much must be done to keep alive King's vision of justice and equality for all people.

"In 1968, Dr. King was fighting for all of us to eliminate injustices and discrimination and segregation," said Barry, himself a former civil rights activist. "The issue of justice was still on the moral agenda because there was great injustice in this land, and there is still great injustice in this world."

Barry said 40 nations are said to be currently at war. He said there is suffering and premature death in Ethiopia, which he recently visited. At home, Barry estimated, some 50 million Americans are impoverished.

"This question of equality of life for all of us," he said, "must be on the moral agenda."