A DA spokesperson said the party would communicate officially when negotiations were finalised.
The third person who died was a 40-year-old man from KwaZulu-Natal province who had mpox-like symptoms including a rash all over his body, the ministry said.
Ramaphosa's African National Congress will be sharing power with five other parties after it was humbled in a May 29 election, losing its parliamentary majority for the first time in 30 years of democracy.
The ANC still has to work out how to divide up the top cabinet jobs and overcome ideological differences with its new partners.
Former president Jacob Zuma's uMkhonto we Sizwe party came in a surprisingly strong third in the May 29 election, which saw the ANC lose its majority.
Once unthinkable, the accord allowed President Cyril Ramaphosa to win a second term in office. He was re-elected by lawmakers with 283 votes.
The SABC report came as the newly elected parliament was convening for the first time and lawmakers were in the process of being sworn in.
Mpox spreads through close physical contact. Most cases are mild but it can kill.
The DA, the largest opposition party, has said it won't join a formation with the EFF or former President Jacob Zuma's uMkhonto we Sizwe (MK) party, which came in a surprising third in last month's vote.
The ANC remains the biggest party, but the lack of an outright majority means it must now share power, and President Cyril Ramaphosa says its leaders decided that a broad collaboration was the best way forward.
The electoral math has created a complex situation for the ANC, which will have 159 of the 400 seats in the new National Assembly.
Spain follows Ireland, which also announced it would intervene in the case.
The South African Health Products Regulatory Authority issued the recall in April, days after Nigeria's regulator recalled the medicine - a batch of Benylin Paediatric Syrup made in South Africa
Trevor Freemantle, who was driving in the area, filmed dark clouds swirling above the suburb of La Mercy near Durban.
The ANC's potential partners are diametrically opposed, ranging from the free-marketeer Democratic Alliance (DA) to uMkhonto we Sizwe (MK) and the Economic Freedom Fighters (EFF).
The result means that the ANC must now share power, likely with a major political rival, in order to keep it - an unprecedented prospect in South Africa's post-apartheid history.
The ANC has lost its outright majority in parliament for the first time since it came to power after apartheid. In the previous election in 2019, the party won 230 seats.
For the first time in South Africa's democratic era, the African National Congress (ANC) will have to seek one or more coalition partners to govern with after it fell well short of a majority in last week's national election.
The party's poor showing has fuelled speculation that Ramaphosa's days might be numbered, either due to the demands of a prospective coalition partner or as a result of an internal leadership challenge.
The ANC has won every previous national election since the historic 1994 vote that ended white minority rule, but over the last decade, its support has slid as South Africans have watched the economy stagnate.