Secretary of State Cyprus Vance will ask South Africa to support the Anglo-American attempt to bring Rhodesia's rival factions into all-party talks to avert a civil war over the former British colony, officials said yesterday.

This latest attempt to invoke the aid of the government most despised by black Africa to try to prevent conflict among Rhodesian nationalist leaders exemplifies the convoluted politics confronting Vance's mission to Africa. South Afirca is still bristling over critisms of its apartheid policy by President Carter during his visit to Nigeria two weeks ago, although Carter stopped short of Nigeria's condemnatory language to try to retain some diplomatic leverage with South Africa.

Vance now plans to go to Pretoria, South Africa, to solicit that nation's help in inducing Rhodesia's white prime minister, Ian Smith, to seek an agreement with the leaders of the black nationlist guerrilas opposing his new multiracial government.

Vance arrived in Tanzania last night after a 19-hour trip form Washington for what reporters aboard his plane were told is very much of a "long shot" in the Rhodesian diplomatic morass. America officials readlily conceded that heading off a larger wat than the present guerilla conflict over Rhodesia "probably may not be achieved." But Vance is convinced the effort must be made.

InTanzania, in South Africa and in Rhodesia itself over the next four days, Vance, U.N. Ambassador Andrew Young and their aides seek to thread a path through a maze of great power and African rivalries.

There is a crazy quilt pattern of alignments to be surmounted. Vance in his initial talks here today will confer first with Tanzanian President Julius Nyerere and British Foreign Secretary David Owen. Along with the Carter administration, Owen has expressed alarm that the Soviet-Cuban projection of military power demonstrated in the Ethiopian-Somali conflict may be extended into southern Africa if there is a failure of diplomatic efforts to achieve black majority rule soon in Rhodesia and in Namibia Southwest Africa.

Tanzania and its fellow "fron-line" states close to Rhodesia support the Patriotic Front guerilla alliance that fought Smith's white minority goverment and now opposes the new government.

Smith has gained the adgantage in this struggle by joining forces very late in the game with moderate black leaders living inside Rhodesia: Bishop Abel Muzorewa, the Rec. ndabaningi Sithole and Chief Joseph Chiray. They are political rivals of the guerilla Patriotic Front's leaders, Joshua Nkomo and Robert Mugabe.

One guerilla group is supported by the Soviet Union and Cuba, while the other is primarily supplied with older Chinese weapons although it also has some Cuban advisers.

The Soviet Union and China are intense competitors in Africa as elsewhere. In effect the United States, Britain and China have been betting on black nationalism over time to counter Soviet penetration of Africa.

The front-line states are all supporting an Anglo-American plan for bringging black majority rule to Thodesia more quickly and effectively than the "internal" settlement devised by Smith. There is the risk, however, that the front-line states may turn to the Soviet Union and Cuba if the Western plan looks like a loser.

What Vance is attempting is to persuade the front-line states and their client, the patriotic Front, to enter an all-party conference with Smith and his three internal black colleagues.

At this stage, Smith and black moderates have rejected that offer, agreeing only to talk with Vance and Owen.

Simultaneouly, South Africa is engaged in the climatic round of bargaining with Western powers over granting independence and black majority rule to Namibia, which South Africa has been governing under an expired mandate from the old League of Nations. Vance hopes to find South Africa prepared to accept a formula for un-supervised elections in Namibia and a U.N. peacekeeping force to replace South Africa's troops.