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Violence in South Africa's black townships is beginning to percolate into the white areas. This is clearly a new factor in the country's 14-month-old black upheaval that the government must deal with both politically and militarily.

The spread of violence to white areas, though minuscule compared with the unrest in black areas, will likely increase the tug and pull on the government. Some whites want Pretoria to get tougher in dealing with unrest. Others are pressing it to start a dialogue with prominent black opponents such as leaders of the banned African National Congress (ANC).

Yesterday, even as the government lifted the state of emergency in 6 of the 36 affected districts, police used a water cannon to disperse Coloreds (persons of mixed race descent), blacks, and a few whites demonstrating in central Cape Town, a designated white area. In a separate incident Thursday police used whips to disperse rampaging youths who had overturned two delivery vehicles in Cape Town.

The spread of violence to white areas was dramatically evident last week when angry blacks and police clashed outside the headquarters of the South African Council of Churches in central Johannesburg. The clash followed a memorial service for the ANC guerrilla Benjamin Moloise.

But the incident, in which two policemen were stabbed, shops were looted, and an elderly white woman was knocked to the ground and robbed of her purse, was not an isolated event. Within a few days there was another outburst of black anger in central Johannesburg when, on Tuesday evening, black youths stoned private vehicles and bus company premises.

On the same night there were episodes of stoning and arson in the white hamlet of Kraaifontein, less than 10 miles from Cape Town. Shots were fired by a white civilian under attack by Colored youths. It was the second time Kraaifontein's whites have come under attack since unrest spread to the western Cape Province in late August.

The attacks have exacerbated white fears, actively encouraged by the government in the past, that the country's black majority would one day swamp whites.

A shopkeeper spoke for many whites when he said after last week's clash in central Johannesburg: ``I have served on the [Namibian] border but I have never been so frightened in my life.''

Dilisa Matshoba, a senior black member of the South African Council of Churches, later warned a meeting of ``concerned citizens'' that the scenes in Johannesburg would become commonplace unless radical changes in South Africa's racial policies took place soon. Already young blacks were firing themselves up to launch attacks in white towns, he told white listeners.

``I have seen pamphlets in Soweto which already say, `to town, to town.' The youths have seen that the police do not use tear gas or shoot so quickly in white towns,'' Mr. Matshoba said.

So far the violence which has brought havoc to the black townships has hardly affected whites in any tangible way. Of the more than 770 people known to have died since the rebellion in the townships began in September last year, only six have been white.

A major proportion of the township violence has been directed against ``black collaborators,'' black men and women seen as the agents of white authority: policemen, prison officers, councillors in the government-approved town councils and, of course, suspected informers.

But, in the end, these blacks are only symbols of white power. The ultimate target is white authority itself, which increasingly appears to mean white civilians.

Attacks on whites so far appear to be spontaneous in some instances and premeditated in others. But at least one prominent black opposition group, the banned ANC, has urged deliberate attacks against certain whites. In a recent message broadcast on Radio Freedom from Addis Ababa, Ethiopia, the ANC urged black household servants in South Africa to steal guns from employers and attack white homes and holiday resorts.

``All along it has only been black mothers who have been mourning,'' the broadcast said. ``Now the time has come for all of us to mourn. Everyone must feel the country is at war and that only the dismantling of the apartheid regime will guarantee everlasting peace and friendship in our land.''

Describing white police and soldiers patrolling in black townships as ``angels of death'' who regard the townships as foreign countries and then ``return to the calmness of their residential areas,'' the ANC broadcast said, ``that myth must be shattered.''

In an interview with the South African newspaper Weekly Mail last month, Steve Tshwete of the United Democratic Front said, ``If the government remains intransigent and the police continue to behave brutally . . . there is every likelihood of the unrest spilling into white areas.'' The UDF is one of the largest, legal black opposition groups in South Africa.

Another sign of growing white concern has been the push by some for dialogue between the government and the ANC. Nico Smith, a controversial Dutch Reformed Church minister, who will lead a delegation of clergymen, is the latest to announce plans to meet with the ANC in Lusaka, Zambia.

Dr. Smith, whose parish lies in the heart of the black township of Mamelodi, near Pretoria, was unmoved by sharp disapproval from President Pieter W. Botha's office. Insisting that the talks could lead only to embarrassment for the South African government, Mr. Botha's office said, ``a continuation of these naive talks, despite appeals by the head of state and his ministers, would amount to a defiance of state authority.''

Smith, however, defended the pending talks, for which no date has yet been set, saying they were indispensable to the reconciliatory role which the church had to assume in South Africa now the government had become, as he put it, ``politically cornered.'' Replying to the charge that it was naive to talk to the ANC, Smith remarked that many thought that Jesus Christ's message of love and forgiveness was childish and naive.

The disclosure that Smith is to head a delegation to Zambia came within a week of the seizure of the passports of eight students at the Afrikaans University of Stellenbosch to prevent them from journeying to Zambia for talks with the Youth League of the ANC.

Afterward the student parliament voted in favor of talks with the ANC Youth League by a ratio of 2 to 1.