South African Prime Minister John Vorster appealed to the American people over the head of the Carter administration last night to oppose U.S. pressure on South Africa. The move indicated a new low in relaions between the two countries as a result of the growing dispute over the issue of change in South Africa's race laws.

Although relations have been cooling for months, Vorster's public blast at the Carter administration - in the toughest langauage to date - amounted to a flat rejection of U.S. policy.

Speaking at a Foreign Affairs Association dinner in Pretoria, the South African leader warned that U.S. policy would lead to "chaos and anarchy in South Africa. If these (U.S.) pressures are insisted on, the end result for South Africa will be exactly the same as if it were subverted by Marxists. In the one case, it will come about as a result of brute force. In the other cases, it will be strangulation with finesse."

Vorster then charged that the Carter policy did not reflect the sentiments of the American people, adding. "As a matter of fact, I believe that once they (the people) realize the possibility of such action, they will demand that it be stooped immediately. I believe sincerely in the fairness and sense of fairness of the American people."

In a clear appeal to the American people he added: "Do not make it impossible for South Africa to play its role in the free world."

Vorster's tough remarks came prior to the scheduled meeting in London next week on Western plans to try to resolve the Southern Africa problem.

Among those scheduled to participate in the session are Secretary of State Cyrus Vance, British Foreign Secretary David Owen and South African Foreign Minister R.F. Botha.

Vorster's stunning statement last night has already been labeled here as "a bombshell for Western plans in southern Africa," since it is viewed as a firm statement of intention not to succumb to Western pressures - or separate development for separate races.

There is also growing speculation that South Africa may be balking at its role in Western-backed efforts to settle Rhodesia's 12-year-old constitutional crisis. After Botha held talks with Rhodesian Prime Minister Ian Smith in Salisbury last week, he told reporters that white southern African leaders were not going to let "outsiders" dictate to them.

South African plays an essential role in the settlement effort since it serves as Rhodesia's only link with the outside world, and has the leverage to force Smith into any settlement plan.

Western diplomats in South Africa were unwilling to comment on the speech or a possible change in South Africa's position. If the analysis by local commentators is correct, however, South Africa has made a complete turnaround.

Just a year ago the Vorster government looked to the United States to solve its problems. Now the U.S. government is viewed as a serious threat to the "peace and stability" of the region.

The change in South Africa's position appears to be the product of the different approaches of the two administrations: Vorster offered a friendly and conciliatory face when former Secretary of State Henry A. Kissinger offered to buy time for South Africa in exchange for help in settling the disputes in two neighboring territories - Rhodesia and Namibia (South West Africa). Now the prime minister is balking, since President Carter has made change in South Africa itself as much an issue of the moment.

The prime minister described the aims of U.S. policy as isolation of South Africa in all fields and discouragement of trade and investment. He charged that the Carter administration's policy was aimed at winning the favor of the Third World, especially black Africa "with its 50 seats in the United Nations."

The government feels that it has been backed into a corner by mounting international pressure, and Minister of Justice Jimmy T. Kruger has even gone as far as to claim that the pressure was at least partially responsible for South Africa's racial unrest.

The moderate, local English-language press has regularly noted the government's withdrawal into a "laager" position in response to the Western push. Laagers were the early defense encampments of South Africa's white settlers during encounters with African tribes).

Forced into a defensive position as never before, the government has begun to strike back, telling both its own angry black population and the outside world that there will be no significant changes.

The government yesterday banned a mass rally called by Soweto's moderate black leaders to try to win mass support for a blueprint of self-rule for the African township. The ban came after another day of unrest when police used dogs and shotguns to scatter stone-throwing teenagers.