Mr Terreblanche, 69, was beaten to death by two farm workers after a dispute over unpaid wages, police say. Two people have been charged.
President Jacob Zuma has appealed for calm, saying the killing should not incite racial hatred.
Mr Terreblanche, who campaigned for a separate white homeland, came to prominence in the early 1980s. He became the champion of a tiny minority determined to stop the process that was bringing apartheid to an end.
"Mr Terreblanche's body was found on the bed with facial and head injuries," said Natal Police Capt Adele Myburgh.
"There was a panga [broad-blade knife] on him and knobkerrie [wooden club] next to the bed."
Capt Myburgh said Mr Terreblanche had been killed at his home outside the town of Ventersdorp, North West province, after a payment dispute with two workers, aged 21 and 15, who have been arrested and charged with his murder.
Mr Zuma condemned the killing as a "terrible deed".
"The president appeals for calm... and asks South Africans not to allow agent provocateurs to take advantage of this situation by inciting or fuelling racial hatred," his office said in a statement reported by South Africa's SAPA news agency.
"The murder of Terreblanche must be condemned, irrespective of how his killers think they may have been justified. They had no right to take his life."
bbc.co.uk
Eugene Terreblanche, the South African white supremacist leader, has been killed on his farm in the country's northwest.
The man whose very name spoke of the apartheid era - it translates as white earth - was one of the country's most polarising figures.
Police have confirmed they now have two young men in custody, both of whom were farm workers employed by Terreblanche.
They are suspected of bludgeoning him to death following an apparent dispute over wages.
South Africa's white supremacist leader Eugene Terreblanche was allegedly bludgeoned to death by two of his farm workers on Saturday in an apparent dispute over wages, police said, amid growing racial tensions in the country. (April 4)
CHARLOTTE - Even by President Obama's loquacious standards, an answer he gave here on health care Friday was a doozy.
Toward the end of a question-and-answer session with workers at an advanced battery technology manufacturer, a woman named Doris stood to ask the president whether it was a "wise decision to add more taxes to us with the health care" package.
"We are over-taxed as it is," Doris said bluntly.
Obama started out feisty. "Well, let's talk about that, because this is an area where there's been just a whole lot of misinformation, and I'm going to have to work hard over the next several months to clean up a lot of the misapprehensions that people have," the president said.
He then spent the next 17 minutes and 12 seconds lulling the crowd into a daze. His discursive answer - more than 2,500 words long -- wandered from topic to topic, including commentary on the deficit, pay-as-you-go rules passed by Congress, Congressional Budget Office reports on Medicare waste, COBRA coverage, the Recovery Act and Federal Medical Assistance Percentages (he referred to this last item by its inside-the-Beltway name, "F-Map"). He talked about the notion of eliminating foreign aid (not worth it, he said). He invoked Warren Buffett, earmarks and the payroll tax that funds Medicare (referring to it, in fluent Washington lingo, as "FICA").
Always fond of lists, Obama ticked off his approach to health care -- twice. "Number one is that we are the only -- we have been, up until last week, the only advanced country that allows 50 million of its citizens to not have any health insurance," he said.
A few minutes later he got to the next point, which seemed awfully similar to the first. "Number two, you don't know who might end up being in that situation," he said, then carried on explaining further still.
"Point number three is that the way insurance companies have been operating, even if you've got health insurance you don't always know what you got, because what has been increasingly the practice is that if you're not lucky enough to work for a big company that is a big pool, that essentially is almost a self-insurer, then what's happening is, is you're going out on the marketplace, you may be buying insurance, you think you're covered, but then when you get sick they decide to drop the insurance right when you need it," Obama continued, winding on with the answer.
Halfway through, an audience member on the riser yawned.
But Obama wasn't finished. He had a "final point," before starting again with another list -- of three points.
"What we said is, number one, we'll have the basic principle that everybody gets coverage," he said, before launching into the next two points, for a grand total of seven.
His wandering approach might not matter if Obama weren't being billed as the chief salesman of the health-care overhaul. Public opinion on the bill remains divided, and Democratic officials are planning to send Obama into the country to persuade wary citizens that it will work for them in the long run.
It was not evident that he changed any minds at Friday's event. The audience sat politely, but people in the back of the room began to wander off.
Even Obama seemed to recognize that he had gone on too long. He apologized -- in keeping with the spirit of the moment, not once, but twice. "Boy, that was a long answer. I'm sorry," he said, drawing nervous laughter that sounded somewhat like relief as he wrapped up.
Some air travelers already uneasy about a range of security checks at the nation's second-busiest airport can add another potential anxiety: The first full-body scanner at Chicago's O'Hare International Airport made its debut Monday.