Nobel Peace laureate Bishop Desmond Tutu told a packed congregation at the Washington Cathedral yesterday that the United States could force an end to South Africa's apartheid policy "tomorrow" by substituting a get-tough policy for the present "constructive engagement."

The black South African bishop challenged people of good will in this country to "make a moral climate in this land that will make it impossible for any administration to cooperate with a system so vicious" as South Africa's official policy of racial separateness.

The 53-year-old bishop touched only briefly on political issues in his sermon, which emphasized the obligation of Christians to work for justice, but at a later press conference was more critical of the Reagan administration's policy.

Responding to a question about the administration's constructive engagement policy, which relies on friendly persuasion to try to get South Africa to change its system of apartheid, he said he didn't know whether South Africa's 22 million blacks "can survive four more years of the kind of medicine we've been receiving."

He said "If we had an explosion now, I wouldn't be surprised . . . . I said on one occasion it was maybe five minutes to midnight. Now I think I can say it's one minute to midnight."

But his eyes caught fire when he was asked about the almost daily antiapartheid demonstrations here and in other major cities. "They are just superb," he beamed. "They warm the cockles of the heart."

Tutu said that this country could force an end to apartheid if President Reagan would demand of South African President Pieter Botha "an end to bannings, an end to all detentions, an end to forced population removals and an end to the denationalizing of blacks -- and tell him that you've had it unless that happens, and then set a specific timetable."

Such a move by the United States would prompt other nations to follow suit, he said. "If the United State coughs, everybody catches cold."

Tutu met with President Reagan on Dec. 7, the day after a group of 35 conservative Republican members of Congress said they would support economic and diplomatic sanctions against South Africa unless immediate steps were taken to end apartheid. Reports at the time indicated that no minds were changed in the conversation.

Yesterday the bishop said that although his visit to the White House "appeared to be intended as a pro forma meeting . . . it turned out to be a great deal of listening" on the president's part.

He fielded a question about whether he felt President Reagan was "morally committed" to ending apartheid with a typical dash of diplmatic humor.

"We always assume you are a saint until it's proven otherwise," he said.

Tutu also smiled when asked if he fears for his safety.

"I work on the assumption that if you are doing God's work," he said, "then it's His business to look after you."

Nearly 2,000 worshipers, many of them standing in the side aisles for a better view, greeted Tutu with uncharacteristic applause when he was introduced by Provost Charles Perry.

The bishop's appearance is expected to be his last here for some time. He has completed his sabbatical in this country, which included a teaching assignment at General Theological Seminary in New York.

Formerly the head of the embattled South African Council of Churches, he returns to his homeland Dec. 31 as Anglican Bishop of Johannesburg, a post to which he was elected last month.

He received the Nobel Peace Prize in Oslo on Dec. 10.