Carrying black cardboard coffins and marching behind a huge "Apartheid Kills" banner, more than 5,000 demonstrators, including New York Mayor Ed Koch, the Rev. Jesse Jackson and actor Paul Newman, staged a symbolic funeral procession to the State Department yesterday in the largest protest here yet against white-ruled South Africa and U.S. relations with that race-torn nation.

The marchers walked from the Washington Monument to the State Department, where they laid 50 coffins at the agency's diplomatic entrance and listened to a multifaith memorial service for black South Africans who have died during escalating violence there.

"It's true, we are gathered at a funeral," said Rabbi Andrew Baker, area director of the American Jewish Committee, who helped lead the service as State Department employes watched from their office windows. "But it is apartheid and not its victims that we come to bury."

The funeral procession, in which about 5,500 persons participated, according to D.C. police, was the biggest antiapartheid demonstration here since protesters began weekday picketing and arrests at the South African Embassy last Nov. 21.

Those arrests, which now number more than 3,000, continued yesterday, even as antiapartheid demonstrators expanded their protest to the State Department and urged the United States to take a tougher stand against the South African government.

"We expect our government to make our national policy consistent with our national ideals," said Randall Robinson, cochairman of the Free South Africa Movement, which launched the embassy protests nine months ago and organized yesterday's funeral march to the State Department's doorstep.

Robinson, executive director of TransAfrica, a black foreign policy lobby, called on the Senate to pass -- and President Reagan to sign -- immediate economic sanctions against South Africa's apartheid system of racial separation.

And he said he puts little stock in recent suggestions that the South African government is about to announce major changes in its policies.

"Sanctions now," Robinson urged. "Prime Minister Pieter Botha and the South African government have a time-honored tradition of making promises they have no intention of keeping."

At a news conference on Capitol Hill before the march, about two dozen political and civil rights leaders took turns lambasting South Africa's apartheid system and the Reagan administration's policy of "constructive engagement" with the Pretoria government. U.S. officials have said, and reiterated yesterday, that quiet diplomacy rather than sanctions is the best way to bring about needed reforms.

But New York Mayor Koch, noting that his city already has begun cutting financial and trade ties with South Africa, compared the official U.S. attitude toward apartheid to the early American response to the rise of Hitler in Nazi Germany. "We were wrong in 1933, and we are similarly wrong in 1985," Koch said.

Koch, said it was "to our eternal disgrace" that the United States abstained on a recent United Nations resolution against apartheid.

Coretta Scott King, widow of slain civil rights leader Martin Luther King Jr., expressed concern about attacks by black protesters against blacks suspected of being apartheid collaborators.

But the violence of blacks against blacks, she said, "is small compared to the every day violence of South Africa's apartheid regime."

Jackson, arguing that South Africa could not exist in a vacuum, said the U.S. government needs to be challenged "to choose the right side of history."

Entertainer Harry Belafonte, a founder of Artists and Athletes Against Apartheid and an organizer of famine relief efforts in Africa, complained that the Reagan administration has been unwilling to take a position of leadership in either the feeding of starving Africans or in the ending of apartheid. "It is unfortunate that our government has played such a weak role," he said.

Others joining the procession included D.C. Mayor Marion Barry; Judy Goldsmith, outgoing president of the National Organization for Women; actor Tony Randall; comedian and activist Dick Gregory; Gerald McEntee, president of the American Federation of State, County and Municipal Employees; Benjamin Hooks, director of the NAACP; Episcopal Bishop John Walker of the Washington Diocese; Imam Sultan Muhammad of the local Islamic community; the Rev. Robert Drinan of Georgetown University's Law Center, and D.C. Del. Walter E. Fauntroy, cochairman of the Free South Africa Movement.

Robinson said those who helped lead the march -- labor, church, civil rights, Hispanic, women and political leaders -- represented a cross-section of the nation and should indicate to administration officials that constructive engagement is out of step with what most Americans want.

Robinson said that with the aid of U.S. protests "no longer will 22 million blacks be landless, rightless and voteless with American support."