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President Cyril Ramaphosa has described South Africa's election results as a victory for its democracy, despite his African National Congress (ANC) party losing its majority for the first time.
The party, which was once led by Nelson Mandela, won 159 seats in the 400-seat parliament, down from 230 in the previous assembly.
It is the ANC's worst election result since apartheid ended 30 years ago - though it still has by far the most seats.
The results announced on Sunday represent a sharp drop in support for the party, which now must go into a coalition to form the next government.
"Our people have spoken, whether we like it or not, they have spoken," Mr Ramaphosa said.
"As the leaders of political parties, as all those who occupy positions of responsibility in society, we have heard the voices of our people and we must respect their wishes."
South Africa's political parties have two weeks to work out a coalition deal, then the new parliament will sit to choose a president.
Former president Jacob Zuma, who now leads the MK party that came third, did not attend the results announcement and had suggested that he might challenge them.
Earlier in the day, Mr Zuma called for an election rerun and said the electoral commission should not announce the final results.
On Saturday, he warned the commission that it would "be provoking us" if it ignored his demand for a fresh election, and for an independent investigation into his party's claims that it was rigged.
"Don’t start trouble when there is no trouble,” he said.
There are now concerns over how Mr Zuma's supporters may respond to the results.
"The results reflect the will of the people," says President Ramaphosa
Earlier, South Africa's police chief warned that threats to destabilise the country would not be tolerated.
"There cannot be any room for threats of instability in order to register objections or concerns about the electoral processes," Police Minister Bheki Cele said at a news conference.
With all the votes in from Wednesday's poll, the ANC finished on 40% - down from 58% at the previous election.
This was lower than the party's feared worst-case scenario of 45%, analysts said.
The ANC has always polled above 50% since the country's first democratic elections in 1994, which saw Nelson Mandela become president.
But support for the party has been dropping significantly because of anger over high levels of corruption, unemployment and crime.