Mr de Klerk, speaking to reporters in Pretoria, said the radical right was planning a day of action on 31 March to step up its campaign for an Afrikaner homeland, the Volkstaat, which could include an attempt to take control of a town.
'We will act firmly against any action or deed which transgresses the law,' Mr de Klerk said.
Mr Mandela's message, delivered to a rally of 20,000 supporters at Mariannhill, 20 miles west of Durban, in Natal, was similarly tough.
'Don't you worry,' he said, 'the peace forces in this country are going to catch up with the hit-squads that are being organised in very high places in this country.'
Mr Mandela was speaking at the start of a four-day tour of Natal province, where Chief Buthelezi enjoys his strongest support. But an Inkatha spokesman, Ed Tillett, said Mr Mandela's visit to Natal was premature and would inflame the already volatile situation in the region. More than 10,000 people have died in political violence in Natal over the past 10 years.
Tomorrow Mr Mandela is scheduled to meet the Zulu king, Goodwill Zwelithini, to discuss his demand for a constitutional monarchy. On Tuesday Mr Mandela said he would be offering the King and Chief Buthelezi a way out of the current impasse.
The warnings by Mr de Klerk and Mr Mandela, the architects of South Africa's transition from white minority rule to fully-fledged democracy, came in the wake of the collapse of the nominally independent homeland of Bophuthatswana and the ouster of its president, Lucas Mangope. Mr Mangope, who had joined the right-wing Freedom Alliance in calling for a boycott of next month's polls, was yesterday put temporarily under house arrest in Motsedi, 90 miles north-west of the Bophuthatswana 'capital', Mmabatho, a restriction that was lifted later in the day.
Both Mr de Klerk and Mr Mandela have been at pains to laud the South African Defence Force for its role in securing Bophuthatswana after armed white extremists attempted last week to seize Mmabatho and neighbouring Mafikeng. The SADF, as when it was deployed in the troubled townships of Katlehong and Thokoza outside Johannesburg in January, was welcomed in Bophuthatswana last week as a liberating force.
With Bophuthatswana now under South African control and the other nominally independent territories, Ciskei, Transkei and Venda, having agreed to participate in the elections, the white extreme right - including Eugene Terre-Blanche's Afrikaner Resistance Movement (AWB) and a faction of the Conservative Party - and Chief Buthelezi's mainly Zulu Inkatha Freedom Party, have remained the spoilers.
Inkatha initially registered for the elections but failed to provide a list of candidates by the deadline last week, thus rendering void its registration. Officials of the Independent Electoral Commission have said that Inkatha's name had been scratched from the ballots, which are being printed in Britain.
Mr de Klerk said his government was planning contingency measures to ensure free elections in KwaZulu, the self- governing homeland run by Mr Buthelezi, the chief minister, who has justified his refusal to participate in the election by what he says is the new constitution's failure to give enough powers to the provinces.
Mr de Klerk refused, however, to say whether he would deploy the SADF in KwaZulu as he did in Bophuthatswana. The decision to do so was expected to be taken only after all attempts at negotiating a compromise with Inkatha had run their course.
Mr Mandela's meeting with King Goodwill tomorrow will be crucial to determining the outcome of those efforts.