Even if agreement is reached on the Cabinet, the ideological differences between the ANC and DA could hinder policymaking down the road, analysts say.
The ANC still has to work out how to divide up the top cabinet jobs and overcome ideological differences with its new partners.
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 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.
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.