Jacob Zuma joined dancers on stage at the ANC garden party in Johannesburg
The African National Congress (ANC) is heading for a decisive victory in South Africa's general election, taking more than two-thirds of the vote so far.
With more than 12 million votes counted, the ANC has 67%.
The major opposition parties are trailing well behind - the Democratic Alliance with 16% and the newly formed Congress of the People (Cope) has 7.6%.
"We know that counting is still going on, but we can smell a 70%," ANC leader Jacob Zuma told jubilant supporters.
The BBC's Peter Biles in Johannesburg says so far the ANC's percentage of the national vote gives the party a fraction more than a two-thirds majority needed to push through constitutional changes.
The ANC is ahead in eight of the country's nine provinces.
Results from some big metropolitan areas, including Soweto, are still awaited. The final results will be declared on Saturday.
The turnout has been extremely high, as much as 80% in some places, in the country's fourth poll and most competitive since the end of apartheid 15 years ago.
In Johannesburg, crowds of ANC supporters dressed in the party's black, yellow and green attended a celebration rally on Thursday evening.
"I would like to thank you for tonight," Jacob Zuma told the crowd, after dancing on stage.
"We went to the voters of this country, talked to them and put across our polices - and they have understood what we are saying," he said.
Parliament will elect South Africa's next president by a simple majority, putting Mr Zuma in line for the post when the new assembly votes in May.
Mr Zuma, a populist who spent 10 years in prison during the apartheid era for ANC membership, faces challenges including a struggling economy and soaring violent crime.
Charges of corruption against the 67-year-old were dropped just two weeks before the poll after state prosecutors said there had been political interference in the case.
The BBC's Africa analyst Martin Plaut says the ANC leader is still something of an enigma - part Zulu traditionalist, part international leader who jets around the world.
During the fight against apartheid Mr Zuma was head of internal security for the ANC, when some people were killed and some tortured.
It is not clear how much he knew or sanctioned, he says.
But Mr Zuma is also a skilled conciliator, credited with ending the political violence in KwaZulu-Natal and helping to bring peace to Burundi.
'Not a rejection'
The election commission said it was pleased with the peaceful way in which the poll was conducted.
The Cope leader, former Bishop Mvume Dandala, told the BBC that the party did not see the result as a rejection. "We are saying that we have been given a critical mass upon which to build," he said.
Cope was formed by ANC dissidents who supported former President Thabo Mbeki, who resigned last year after losing a power struggle with Mr Zuma.
Analysts say Cope's emergence energised the early stages of the election campaign but the party's popularity seems to have diminished in recent weeks.
It is thought that Cope and the DA could enter into a coalition after the election, presenting a real threat to the ANC's continued dominance of South Africa.