Bishop Desmond M. Tutu, the 1984 Nobel peace laureate, was today elected Archbishop of Cape Town. He becomes the first black man to head the Anglican Church in southern Africa.

His election was announced after barely nine hours of a scheduled four-day meeting of the multiracial church's elective assembly, indicating an unexpected degree of support from white members for the outspoken black bishop.

Opposition from white members was predicted because of Tutu's call two weeks ago for international sanctions against South Africa, but it did not materialize. Assembly sources said Tutu easily gained the required two-thirds majority of both clergy and lay members voting separately.

As Archbishop of Cape Town, Tutu will be the spiritual leader of about 2 million Anglicans in an area that includes South Africa, Lesotho, Swaziland, Mozambique and Namibia.

Four-fifths of the church's members are black, but the one-fifth whites exercise disproportionate influence because they contribute 80 percent of the church's funds. There were warnings that if Tutu were elected white donations might dry up, plunging the church into financial trouble.

"I am overwhelmed and deeply shattered by the enormous responsibility that has been placed on my shoulders by God," Tutu told a news conference in Cape Town after his election.

He renewed his commitment to work for fundamental political change in South Africa, but tried to allay white anxieties by saying he would be guided by his counselors and was "not a one-man band about to explode on the scene."

Asked whether the church as a whole would adopt a stand in favor of sanctions and disinvestment under his leadership, Tutu noted that a provincial assembly was due to meet on this issue in November.

Tutu, 54, will become archbishop in September when the present head of the church, Phillip Russell, retires. He will move to Cape Town, relinquishing his present position as Bishop of Johannesburg, which he has held for only 14 months.

Although black colleagues in the church expressed delight and pride at his election and the increased influence it will give him, many also said they were dismayed that Tutu would be leaving South Africa's main metropolitan region, which is the focal point of its racial conflict.

Tutu said before the election that he did not want to leave Soweto but had been pressured by black colleagues into allowing himself to be nominated.

Observers see his easy election today as evidence that Tutu is gradually overcoming the intense hostility white South Africans have long shown toward him. Although Tutu is regarded as a moderate abroad, whites here see him as an extremist because of his outspokenness. He is repeatedly portrayed as an advocate of violence because of his frequent warnings that apartheid provokes black violence.

Tutu was nominated to be Archbishop of Cape Town in 1981, but white opposition prevented his election. After a brief deadlock in the elective assembly, Russell was chosen instead. Whites again opposed Tutu when he was nominated to be Bishop of Johannesburg after winning the Nobel prize. They prevented him from obtaining the required two-thirds majority in the elective assembly, but he was eventually selected by a synod of bishops.

One elective assembly source described Tutu's swift election today as "quite remarkable" and asign of growing unity between blacks and whites in the church.

Police reported tonight that 14 black persons had died, including five shot dead by police, in continued racial violence throughout South Africa during the past 24 hours, and the bodies of another 36 thought to have died sometime last month had been found in a tribal "homeland" north of Pretoria.

Six of those who died yesterday and today were burned when their houses were set on fire in a black township near the port city of East London. Another three, accused of being police informers, died in "necklace" executions with gasoline-filled tires pulled over their bodies and set ablaze.