JOHANNESBURG, SEPT. 14 -- Black nationalist leader Nelson Mandela met today with President Frederik W. de Klerk, and both men said afterward that the South African president plans comprehensive action to stem a wave of violence that has claimed more than 700 lives in black townships in the past six weeks.

Mandela, deputy president of the African National Congress, said de Klerk now believes that the strife in black townships near Johannesburg has been manipulated by a "hidden hand" or "third force." Mandela declined to identify the outside forces that he said de Klerk views as a factor in the violence.

The ANC, South Africa's most prominent black nationalist group, has repeatedly charged, however, that white extremists, including members of the government's security forces, have played a role in the conflict. At his news conference today, Mandela underscored this contention, saying he suspects "right-wing members of the security forces."

Today's meeting in Pretoria, South Africa's administrative capital, was the second between the two leaders in four days. De Klerk later said he will announce plans early next week for "strong and comprehensive action" to end the violence. Although de Klerk did not elaborate, Mandela said the announcement would likely occur Monday.

Hours after their meeting, renewed violence took place. For the second time in two days, an attack was reported on a commuter train. Assailants were reported to have hurled passengers from the train as it pulled out of a suburban Johannesburg station, leaving 15 people injured. Later tonight, there was an unconfirmed report of another train attack near the same station.

Thursday night, 26 people were reported killed and more than 100 injured during a rampage by six men aboard a rush-hour train filled with black commuters.

In a separate incident involving commuters in South Africa's industrial heartland, five men were reported to have been shot fatally early today when gunmen opened fire on minibus taxis in Soweto, a black Johannesburg suburb.

At his news conference, Mandela declined to disclose what evidence had led de Klerk to what he described as the South African president's conclusion that outside forces were fanning the violence. For weeks, the government has denied the ANC's allegations of involvement by whites, including security force members. But Mandela made clear that he suspects right-wing security officers who, he said, want to destabilize the negotiating process underway between the government and the ANC over a new South African constitution that would allow the black majority to share power with whites.

Mandela charged that such agents have sought to exploit a long-standing political rivalry between followers of Zulu Chief Mangosuthu Buthelezi's Inkatha Movement and the ANC. The recent violence in black townships has been widely viewed as an outgrowth of a three-year conflict between Inkatha and ANC supporters in Natal province.

Mandela said de Klerk's acknowledgment made it clear that the violence did not stem solely from conflicts among blacks, between Inkatha and the ANC, or between members of the Zulu and Xhosa tribes, as the government has suggested and as local media have reported. "Inkatha continues to be used by these {right-wing} elements that are fueling the violence," Mandela said.

In a speech tonight at a Johannesburg synagogue, Mandela said, "There is no doubt in my mind -- and all the evidence conclusively supports this -- that the police and sectors of the government are working with a variety of vigilante forces, including Inkatha."

Warning that South Africa faces grave dangers as well as great possibilities, Mandela declared, "On the eve of real negotiations, forces determined to wreck the peace process have implemented a strategy of destabilization, which has resulted in the very real and terrifying prospect of full-scale civil war breaking out."

At his news conference, Mandela suggested that security forces suspected of playing a role in the violence may be linked to elements supporting the insurgent Mozambique National Resistance, known as Renamo.