Fifty-seven more black South Africans were killed in tribal clashes and other violence today, bringing the country's casualty toll over the past 16 months to more than 1,000.

Fifty-three of the Christmas Day deaths resulted from a clash between two black groups in Umbumbulu, a township south of Durban.

Three blacks died in attacks by black militants on others whom they regard as collaborators in the apartheid system of segregation. One man died when police opened fire several times on demonstrating crowds in a township 36 miles north of Cape Town.

There has been no immediate explanation of the fighting that led to the deaths in Umbumbulu, the Zulu word for bullet.

Police officials said they were the result of tribal clashes between Zulus and members of a subgroup of the Xhosa tribe known as the Pondos.

But many Xhosas in the Durban area are migrant workers from the Transkei tribal homeland, who come into conflict with local Zulu workers.

The situation is aggravated by the fact that most Zulus support the Inkatha movement, led by Chief Gatsha Buthelezi, while many Xhosas, who belong to the tribe of imprisoned African National Congress leader Nelson Mandela, are supporters of the rival United Democratic Front.

The two movements have been coming into increasingly violent conflict lately, although it was unclear whether the clashes last night and today were the result of political differences or were motivated by nonpolitical factors.

Today's clashes with the police took place in the picturesque town of Paarl, headquarters of South Africa's wine-making industry and one of the oldest centers of white settlement in the country.

The police tried repeatedly to disperse demonstrators who kept reassembling in Mbekweni, the town's black quarter. Eventually police opened fire with shotguns and rubber bullets, killing a man, according to a police report.

One of the blacks killed by militants died in Guguletu township outside Cape Town. His death resulted from what has come to be known as a "necklace" killing. The victim is stoned or beaten unconscious; then an automobile tire filled with gasoline is pulled over his body and he is set on fire.

The other two killed by militants died when their houses were set on fire -- one in Kwamashu township outside Durban, the other in the small town of Hanover in eastern Cape Province.

Three other blacks were injured in the eastern Cape Province town of Stutterheim when militants set fire to their house.

Meanwhile, the South African Jewish Board of Deputies today issued a statement condemning Monday's bomb attack that killed six whites and injured 61 in a shopping center south of Durban.

"We hope and pray that during this season of good will all the peoples of this land and their leaders will be influenced by a spirit of reconciliation and turn toward negotiation as a means of resolving those issues that stand in the way of a harmonious society and the realization of this country's full potential," the board's chairman, Michael Katz, said in the statement.

In a Christmas Day sermon at St. Mary's Episcopal Cathedral in Johannesburg, Nobel Peace Prize winner Bishop Desmond Tutu called on South Africans to work to bring peace and justice to their country.

Tutu told a congregation of about 400 people including blacks and whites that Christ had left them to continue his work.

"How can we go on like this?" he asked. "With a state of emergency, soldiers in the townships, tear gas and rubber bullets, people being burned, homes being gas-bombed, people being intimidated, people being detained without trial. . . . "

He pleaded, "Let us work so that Christmas 1986, unlike Christmas 1985, will be one where all of us, black and white, will be able to say indeed God is with us."

In another Christmas development, Winnie Mandela made a visit to her husband, Nelson, at Pollsmoor Prison in Cape Town.

Nelson Mandela, 67, whose African National Congress opposes apartheid, has been in prison for 23 years, serving a life term for treason and sabotage.

After their 40-minute meeting, Winnie Mandela told reporters that "this past Christmas is far worse than any other Christmas in prison because he was in solitary confinement."

Her husband had seen a fellow inmate only once since being returned to Pollsmoor after undergoing prostate surgery last month, Mandela said.

"He is now held in solitary confinement under the pretext that he is in prison hospital. There is no justification at all for him being held in solitary," she said.

With Mandela was her daughter, Zinzi, and attorney Akbar Ayob.