NEW YORK, SEPT. 29 -- Secretary of State George P. Shultz, arguing that South Africa's racial problems cannot be changed by outside pressures, tonight challenged all "South Africans to rise to the test of building a future" based on democracy and an end to apartheid.

In a speech here, Shultz gave what amounted to a lengthy restatement of the Reagan administration's 6 1/2-year policy of pursuing change in South Africa through persuasion rather than confrontation with Pretoria's white minority government.

"A long-entrenched system of racial oppression must and will be replaced," Shultz told the Business Council for International Understanding. "This can be done without, in the process, destroying a society and economy that can offer better lives for all South Africans."

"The hard work is up to the South African people themselves," he added. "The time has come for South Africans to act on their hopes, not their fears. They will find a friend in the United States when they do so, a friend that is realistic in its understanding, hopeful in its expectations and optimistic in its vision of what they can achieve."

A senior State Department official closely involved with African policy-making called the speech "an important statement of policy that will send a strong signal to South Africans about what the United States is for."

The official, who asked not to be identified, said the speech sought "to avoid revisiting old battles." He was referring to past controversies that have caused the administration to be criticized severely by black Africans and that last year prompted Congress to override President Reagan's objections and impose economic sanctions on South Africa.

The 22-page text of Shultz's speech did not mention the word "sanctions."

The official said a report on the first year of sanctions, which restrict South African exports to this country and ban new U.S. investment there, will be sent to Congress on Friday.

The official would not discuss details of the report. But he said it would underscore the fact that no progress has been made toward ending racial oppression since the sanctions were imposed. He also said the report would buttress the administration's contention that pressure is the wrong way to deal with the problem.

On another point of administration policy that has been harshly criticized by American civil rights activists -- investment by U.S. businesses in South Africa -- Shultz's speech spurned the calls for disinvestment that have caused growing numbers of U.S. firms to end their activities there.

"American corporations, often maligned for even being in South Africa, can be proud of being in the forefront of the forces for change," he said.

He did not mention that the Rev. Leon Sullivan, a Philadelphia clergyman whose "Sullivan principles" were the widely accepted guidelines under which most American firms operated, recently recanted his view that U.S. investment can help effect change in South Africa.

Shultz, citing a tendency toward "a debilitating pessimism" about South Africa's future, emphasized factors in the South African situation that he said give cause for optimism about "our vision of the future."

The list enumerated by Shultz of "what we are for," however, consisted of an endorsement of pluralistic democracy without racial discrimination and with guarantees of civil and human rights.

And in discussing U.S. efforts to help bring about that process, Shultz made clear that the administration does not intend to move beyond its past practice of "encouraging peaceful change" through quiet diplomacy.

He described U.S. policy as meeting with all parties and encouraging them to engage in dialogue, "working with the victims of apartheid" through financial aid to help them develop "leadership skills and self-empowerment," supporting "an active private American presence to promote racial equality" and working with our allies "to assert our vision of the future."