South African opposition parties said on Friday they were waiting for more details on a proposal by the African National Congress (ANC) to form a government of national unity after it lost its majority for the first time in the democratic era.

The former anti-apartheid liberation movement once led by Nelson Mandela has run South Africa since 1994. But voters, angered by years of economic stagnation, high unemployment and corruption, punished it at the ballot box on May 29.

It remains the biggest party. But the lack of an outright majority means it must now share power - and President Cyril Ramaphosa said on Thursday the ANC leadership had decided that a broad collaboration was the best way forward for South Africa.

The Democratic Alliance (DA), the largest opposition party, said it was open to talks and was "committed to the process".

"But the broad invitation to all parties ... rather than limiting it to parties committed to our current constitutional dispensation, the rule of law and a social-market economy, has undoubtedly complicated matters," spokesperson Werner Horn said.

"Our negotiation team will ... have further meetings with other parties to listen to their views and reaction," Horn added.

The ANC will have 159 of the 400 seats in the new National Assembly. Its nearest rivals are the pro-business, white-led DA, with 87 seats; the populist uMkhonto we Sizwe (MK) led by former President Jacob Zuma, with 58; and the hard-left Economic Freedom Fighters (EFF) with 39.

Ramaphosa said the ANC had already held constructive discussions with the EFF and DA, as well as with the smaller Inkatha Freedom Party (IFP), the National Freedom Party and the Patriotic Alliance.

Zuma's MK said it expected to meet with the ANC soon.

During the election campaign, the DA had called any potential ANC tie-up with the EFF or MK a "doomsday coalition" that would tank the economy. Both smaller parties advocate nationalising mines and seizing land without compensation.

The EFF said it would not be part of a government involving the DA.

"We are not desperate for positions in government," its deputy leader Floyd Shivambu told a press conference.

The socially conservative IFP, which has its power base among South Africa's Zulu people, said it was not averse to the proposal of a national unity government.

"However, the devil is in the details, which will become clearer in the coming days," it said in a statement.

The powerful Cosatu trade union group, a major ANC ally, said it would engage with the ANC and another backer Communist Party in the coming days, including on the various "permutations and modalities" that would need to be in such a government.

The new parliament has to convene within two weeks of Sunday's results declaration and one of its first acts must be to elect the president.

The constitutional deadline, which will fall on or near June 16, is putting pressure on the ANC and others to reach an agreement quickly.