Thabo Mbeki, the ANC national chairman and likely heir to Nelson Mandela as ANC president, led a delegation at the start of two days of talks with General Constand Viljoen and other senior Volksfront officials.
An AVF spokesman, Koos van Rensburg, was surprisingly upbeat in an interview with Reuters. 'We think our chances of agreement are better than 50 per cent. We are absolutely determined to find a solution in a negotiated way. The alternative is unthinkable.'
Signalling a dramatic softening in the position of the AVF, a right- wing umbrella body that includes the parliamentary Conservative Party and Eugene Terre-Blanche's Afrikaner Resistance Movement (AWB), Mr van Rensburg indicated that demands for an independent Afrikaner state within South Africa's borders had been dropped.
'We are not looking at ourselves as a sort of independent state. We want the political ties to be as loose as possible but we will stay in other matters in a united South Africa.'
These were not the sort of noises General Viljoen was making at a rally in Pretoria timed to coincide with the ratification of the new constitution on Wednesday night. As has become customary, the former chief of the South African Defence Force told a rally of right-wingers that South Africa was on the brink of war. 'We are in a disastrous situation tonight,' he said.
Afrikaners had to undergo military training and prepare to defend themselves against attack both during the build-up to the April election and the five years after when South Africa would be run by a 'Communist' ANC government.
However, having fed his followers their traditional rhetorical fare, he eased up towards the end of his speech. Negotiations would continue, he said.
'We are keen for a solution between the Afrikaner and the African. We have arrived at a crucial stage. ANC leader Nelson Mandela should accept our sincerity in our effort to address problems.'
If, for all the bluster, the hope does exist of a solution to the anxieties of right-wing Afrikaners, it is in part because of a quiet bilateral deal the ANC made with the government on Wednesday as the final details of the constitution were being discussed at the multi-party Negotiating Council.
It was agreed that within the terms of the federal system that will come into place after the elections, each of the nine provinces would be entitled to draft its own constitution, so long as the laws fell within the parameters set out in the new national constitution.
That constitution - it will be passed into law next month by the existing parliament - has left deliberately vague the question of provincial boundaries.
The possibility therefore remains that if the Volksfront comes up with a map of a province where it feels Afrikaners might naturally be in a majority, a solution might be found that was acceptable to the ANC.
Nelson Mandela set out the condition for such a solution in his speech to the 21 parties that drafted the new constitution on Wednesday night.
'Let this, however, be clear,' he said. 'There is no place in a democracy for any community or section of a community to impose its will at the expense of the fundamental rights of any other citizen.'
His message, clearly directed at the Afrikaner separatist camp, was that any form of institutionalised racial discrimination would not be accepted. Adding momentum to South Africa's democratic drive, and at the same time putting pressure on the Volksfront and its Inkatha Freedom Party allies to participate in the elections, was the fulsome response of the international community to the news of the new constitution.
The impact of the tidal wave of congratulations that flooded in yesterday from the US and British governments, from the European Union, the Commonwealth and the United Nations will be felt most strongly among South Africa's insecure and uncertain white community - the constituency, English- speakers as well as Afrikaners, whose hearts and minds are not yet at peace with the idea that Nelson Mandela will be president within six months.