The country had called for their total elimination in all international forums, she said.
Suggestions that South Africa had made a U-turn on its nuclear stance were a "figment of the imagination".
In its Analysis column on Friday, The Star reported that South Africa had softened its anti-nuclear stance to strengthen a South-South alliance.
Columnist Peter Fabricius wrote that until now, South Africa had always countered India's stance of not abandoning its nuclear programme before others did, by arguing that all countries should disarm, and that in the meantime there should be no new nuclear powers.
However, he said, a recent India, Brazil, South Africa (Ibsa) declaration suggested "that India need not scrap nuclear weapons until the official powers do".
"The reason for this shift seems to be because the strategic importance of India within Ibsa -- the core of a South-to-South alliance to counter the disproportionate influence of the North -- outweighs SA's disarmament misgivings," he wrote.
Dlamini-Zuma said in a statement that the three Ibsa heads of state had in the declaration emphasised their commitment to complete elimination of nuclear weapons.
They had also expressed concern over the lack of progress in realising this goal.
This was Ibsa's traditional position and was reflected as such in a similar declaration made a year ago.
She rejected the assertion that South Africa had "finessed" its position.
A suggestion that the three countries reserved their right to manufacture nuclear fuel failed to take into account that India had done so for decades and that Brazil was already enriching uranium.
"South Africa remains opposed to the view that the right to peaceful nuclear technology should be a preserve of the rich and powerful...depriving the have-nots in perpetuity," said Dlamini-Zuma.
She said the three Ibsa leaders had reiterated the importance of ensuring that any "multilateral decisions" related to nuclear fuel did not undermine countries' right to pursue nuclear energy for peaceful purposes.
In his column, Fabricius wrote that a resumption of fuel production by South Africa would be fine if economically feasible, but would be "too much like a return to the apartheid days" if it was done only to establish strategic independence from existing fuel producers.
"Southern independence from the North is no doubt a good thing. But at what price?" he asked.
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