Sen. Richard G. Lugar (R-Ind.), incoming chairman of the Senate Foreign Relations Committee, yesterday called on President Reagan to denounce apartheid "much more sharply and more often."

But other members of Congress called for more forceful action to try to influence changes in South Africa's system of racial segregation, with Sen. Daniel Patrick Moynihan (D-N.Y.) saying that "our government should have nothing whatever to do with it the South African government ."

Moynihan and Lugar appeared on NBC's "Meet the Press".

South African Bishop Desmond M. Tutu, who is to receive the Nobel Peace Prize in Oslo today, meanwhile predicted that if the United States does not pressure the South African government to end apartheid peacefully, "we're going to have a blood bath."

"Everyone will be involved in the bloodshed , and it may be that a white skin will be a horrible disadvantage," Tutu said, appearing on ABC's "This Week With David Brinkley".

Reagan's policy of "constructive engagement," attempting to influence South African racial policies through diplomatic channels rather than with punitive actions, such as diplomatic or economic sanctions, has come under increasing criticism here.

About 350 people demonstrated outside the South African Embassy on Massachusetts Avenue, but no one was arrested. Civil rights leaders began a series of protests and planned arrests here Nov. 21 in response to rising violence and the detention of labor leaders in South Africa over racial issues.

But yesterday's demonstration was organized by a group from St. Augustine's Catholic Church here.

After meeting with Tutu on Friday, Reagan reaffirmed his policy of "constructive engagement" and said it would continue. But he added that he would look carefully at suggestions made by the bishop, a prominent antiapartheid leader.

"The president feels that apartheid is abhorrent," Lugar said. " . . . He needs to say so much more sharply and more often that there be no ambiguity . . . .

"I hope the president will, and I'm fairly confident that he is prepared to do so."

But Lugar voiced skepticism about the ability of the United States to force action by South Africa through legislation, such as proposals to limit future investment there by U.S. businesses. These "might have some minimal effect. But my own judgment is that the government of South Africa is going to move at about its own speed and in its own interests," Lugar said.

Moynihan said the U.S. government should cut off contact with the white-ruled South African government but that individual Americans should go to South Africa to be in contact with the black majority to let the government know that the United States supports "the decent elements."

Tutu said that constructive engagement has not worked and that American businesses in South Africa could use their leverage more effectively.

"And I don't understand people who say economic sanctions don't work, especially in a country that has applied sanctions against Poland and is applying, over a very long period of time, an embargo on Cuba," he said.

Rep. Newt Gingrich (R-Ga.), one of 35 conservative House Republicans who warned South Africa last week that they would support sanctions unless there is movement soon to end apartheid, said South Africa must make a systematic transition to an integrated society.

"The only alternative is absolute bloody violence on an unimaginable scale in which the United States in the end is not going to be on the side of the current governing force in South Africa," Gingrich said.

Rep. John Conyers Jr. (D-Mich.), one of those arrested at the embassy, said the United States must stop supplying South Africa with military support and nuclear equipment, and he called for an end to U.S. investment in South Africa.

Assistant Secretary of State Chester A. Crocker, appearing on the Brinkley show after Gingrich and Conyers, said the United States has no military relationship with South Africa. Conyers said in a telephone interview later that he would soon document U.S. military aid to South Africa.

Bernardus Fourie, South Africa's ambassador to the United States, said on the same program that the one man-one vote principle "is not the answer in South Africa. We've got to work out a different system."

He said South Africa realizes that everyone there should have "a reasonable part in political participation."