At 0940 GMT, the rand traded at 18.2150 against the dollar, about 1.4% stronger than its previous close. The currency fell sharply on Thursday after local media reports suggested that a deal between the two parties - the largest in the unity government - was in jeopardy.
A DA party source close to the talks noted that the party was still committed to negotiations over cabinet posts and was "not at the point of drawing lines in the sand and giving final ultimatums".
The comments came after the News24 website and the Business Day newspaper had reported that the ANC had backtracked on an offer to give the DA the trade and industry ministerial portfolio, angering the DA.
Financial markets are on edge over the composition of the cabinet as it will give an early indication of how the ANC intends to share power in the government of national unity (GNU) that emerged after the ANC lost its parliamentary majority in an election last month.
"It has been quite a recovery this morning," said Danny Greeff, co-head of Africa at ETM Analytics, of the rand. "The continued negotiations are certainly welcome, as they suggest that both the ANC and the DA are still intent on making a more centrist GNU work."
"The most likely outcome thus remains for the ANC and DA to reach an agreement. Depending on what that agreement entails, we could see the rand extend its previous rally," he added.
ANC and DA officials had noted earlier this week that the cabinet was likely to be announced on Wednesday or Thursday, however it is still not clear when it will be made public.
On the Johannesburg Stock Exchange, the blue-chip Top-40 index traded over 1% stronger. South Africa's benchmark 2030 government bond was stronger, with the yield down 22 basis points to 9.905%.
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