The state that Rep. Robert S. Walker (R-Pa.) represents was reported incorrectly Thursday.

President Reagan will meet privately this week with Bishop Desmond M. Tutu to discuss administration policies on South Africa, White House officials said yesterday, while 35 conservative Republican congressmen warned South Africa they will support diplomatic and economic sanctions against that country unless it takes immediate steps to end its apartheid system.

"South Africa has been able to depend on conservatives in the United States . . . to treat them with benign neglect" in the past, said Rep. Vin Weber (R-Minn.). "We served notice that, with the emerging generation of conservative leadership, that is not going to be the case."

The new position, conveyed in a letter hand-delivered to South African Ambassador Bernardus G. Fourie at the office of Rep. Robert Walker (R-Ill.), follows a series of growing protests against apartheid and arrests of liberal Democratic congressmen and civil rights leaders at the South African embassy here.

Reagan's meeting with Nobel Peace Prize winner Tutu, tentatively scheduled for Friday, would be his first with a black South African opponent of that nation's segregationist regime.

The Reagan administration has pursued a policy of "constructive engagement," designed to influence South Africa gradually to change its policy of racial segregation through friendly persuasion rather than punitive actions, such as economic sanctions.

While there is no indication that Reagan is considering abandoning that policy, recent violence in South Africa and the protests here and in other American cities have made that policy politically embarrassing.

The strong warning by the 35 Republicans, who generally are Reagan allies, signaled a significant movement on Capitol Hill for a more aggressive policy toward South Africa.

Rep. John Conyers (D-Mich.), one of the liberal black congressmen arrested at the embassy here, called the conservatives' letter "an extremely strongly worded message" that could make a difference in gaining passage of legislation to change U.S. policies.

"This move is at least the first step in making this a bipartisan or a nonpartisan issue," Conyers said of the letter.

"We are looking for an immediate end to the violence in South Africa accompanied by a demonstrated sense of urgency about ending apartheid," the letter said. Without these actions, the group will recommend curtailment of new American investment in South Africa and international diplomatic and economic sanctions against the country, it said.

"We wish to be able to endorse policies that produce stronger ties between our two nations. But the reality of apartheid and the violence used to keep it in place make it likely that our relations will deteriorate," the letter said.

Constructive engagement merits support only "as long as real steps toward complete equality for all South Africans are ongoing," it said.

Walker said the group would support legislation to invoke sanctions next year unless the end of violence is "immediate" and South Africa makes "real progress" on human rights.

Rep. Newt Gingrich (R-Ga.) said the group wanted to make it clear there "is no base of any kind in the United States for long-term relationships" with a society in which one group oppresses another and that South Africa must move rapidly to a "multiracial, integrated, free society" if it is to maintain its ties with the United States.

The congressmen declined to attack the Reagan administration for its current policies, however. Rep. Dan Coats (R-Ind.) said the administration may be making gains privately that have not yet come to light.

Ambassador Fourie had no substantive response for the group but planned to convey the message to the South African government, the congressmen said. "I think he was surprised to hear it the message from conservative members of Congress," Weber said.

Tutu, who is to receive the Nobel Peace Prize in Oslo next week, has charged that the Reagan administration's current policy of constructive engagement is "immoral, evil and totally un-Christian" collaboration with South Africa's apartheid system and has worsened the plight of blacks in that country.

On Tuesday, Tutu told a House subcommittee he wanted to meet face to face with Reagan to try to persuade him to change his South Africa policies.

"We look forward to the meeting and the exchange of views it will provide," said an administration official. "It will associate the United States publicly with the view we have expressed privately to South Africa, which is that apartheid must yield to peaceful change."

Some officials also acknowledge that the nonviolent protests have helped demonstrate the depth of U.S. distaste for the South African system.

"The demonstrations and the Reagan-Tutu meeting can send a useful message," one official said yesterday.