DURBAN, SOUTH AFRICA, JULY 7 -- As tens of thousands of black South Africans marched through this and a dozen other cities today to protest the continued violence in Natal Province, the African National Congress appeared to be considering an offer to suspend its armed struggle against apartheid in return for government action to end violence against the black nationalist organization.

Speakers at the marches and rallies today said the government action should include disarming white extremist organizations threatening to launch a guerrilla war against black nationalists, ending police violence against blacks and disbanding a police force serving Chief Mangosuthu Buthelezi's Kwazulu homeland, located in Natal.

Although there have been no attacks by the ANC's guerrilla wing, Spear of the Nation, since President Frederik W. de Klerk legalized the black nationalist organization last February, the armed struggle, as it is popularly called, remains officially in operation and has become an emotional issue clouding the climate for negotiations that de Klerk is trying to create.

To blacks it is an emotionally important symbol of their long struggle against the white regime and a crucial insurance against any backtracking by de Klerk. Whites see it, with equal emotional intensity, as evidence of bad faith on the part of the ANC.

Both President Bush and British Prime Minister Margaret Thatcher urged the ANC deputy president, Nelson Mandela, to renounce the armed struggle when they met him during his recent tour of the United States and Western Europe. Among other arguments, they suggested that this might help de Klerk counter the alarming growth of white right-wing opposition to his reform policies.

Speculation that the ANC may be considering this as part of a tradeoff deal was sparked by reports from diplomatic sources in London that Mandela told Thatcher at their meeting July 4 that the ANC was ready to negotiate a suspension of the armed struggle when it resumed "talks about talks" with the de Klerk government.

In a further statement today, Mandela was reported from Kampala, Uganda, saying these talks would resume July 18, the day he is scheduled to return from his six-week international tour.

Meanwhile, ANC headquarters in Johannesburg announced that today's marches were part of a campaign that would culminate in a meeting with de Klerk to discuss the violence in Natal, in which about 3,500 people have been killed in the past three years.

No date for this meeting was mentioned, but speakers at the rallies repeatedly linked the Natal violence with the resumption of the "talks about talks," hinting that the ANC and its allies intended to make effective government action to end the violence against them a new precondition for their participation in negotiations to draft a new post-apartheid constitution.

"We call on de Klerk that negotiations are not going to continue while this senseless violence continues in Natal," said Thami Mohlomi, a pro-ANC labor leader who was the keynote speaker at the Durban rally.

The most specific demand at the rallies and marches was that the Kwazulu homeland police be disbanded and merged into the regular South African police force. Describing the homeland police force as the "armed wing" of Buthelezi's Inkatha Movement, speakers said it was unacceptable that the ANC should be asked to demobilize its military wing while the Kwazulu police force was allowed to continue operating.

Noting that the Kwazulu police fell under the direct command of Buthelezi, the homeland's minister of police as well as chief minister, S'busiso Ndebele, regional secretary of the ANC, told the rally that it was impossible for such a force to be an impartial peace-keeper in the region.

"This is Buthelezi's legalized, private army," he said. "The Kwazulu police must be disbanded and Inkatha must be like us, an ordinary party without arms."

If the government did not concede that, then the ANC could not be expected to suspend its armed struggle, he added.

Political observers said the thrust of the campaign, seen together with Mandela's statements abroad, pointed to an ANC attempt at the July 18 talks with de Klerk to offer a suspension of the armed struggle in return for a merging of the Kwazulu police into the general South African police force, together with pledges by de Klerk to discipline his own police and take tougher action against white extremists.

About 10,000 people attended today's rally in Durban, Natal Province's biggest city. After hearing speeches on a sports field, they marched three miles through the city to the provincial police headquarters where they presented to the police chief, Col. Kobus le Roux, a memorandum addressed to de Klerk.

The memorandum called for a judicial commission of inquiry into the causes of the Natal violence, claiming this would establish that Inkatha was the primary aggressor.

Similar rallies were held in Johannesburg, Cape Town, Pretoria, Port Elizabeth and smaller cities around the country.