AWB supporters accuse the ANC's Julius Malema of inflammatory actions
The party of murdered South African white supremacist Eugene Terreblanche has withdrawn a threat to take revenge for his death.
AWB spokesman Pieter Steyn said no member of his organisation would engage in any form of violence.
The remarks come after officials from the ruling ANC paid their respects to the Terreblanche family and President Jacob Zuma issued a call for calm.
Police say his murder on Saturday was caused by a dispute over workers' pay.
Supporters of the AWB - Afrikaner Weerstandsbeweging or Afrikaner Resistance Movement - blamed provocative actions by the ANC youth leader, Julius Malema, for the killing.
Last week, Mr Malema was banned from singing a song with the words "Kill the Boer, kill the farmer."
Mr Terreblanche, 69, was fiercely opposed to the end of apartheid in South Africa, which led to the ANC winning the country's first democratic elections in 1994 and Nelson Mandela becoming the country's first black president.
Earlier, the AWB's secretary general, Andre Visagie, had described Mr Terreblanche's killing as a "declaration of war" by South Africa's black community.
"The next step for the AWB will be to bury their leader in peace, but thereafter we shall avenge the death of our leader," he told the BBC on Sunday.
But speaking at the gate of Mr Terreblanche's farm on Monday, Mr Steyn said the threats had been made out of anger and were now being retracted.
"It is the philosophy of the AWB that no member of the AWB will engage in any form of violence, or intimidation, or racial slandering, or anything of that matter," Mr Steyn, a general in the AWB, told the BBC.
"We appeal for people to remain calm. Anyone engaging in any form of violence is not doing it as AWB."
Visits to the Terreblanche farm by senior ANC figures and the televised appeal for calm and restraint seemed to have reassured the far-right movement that their concerns are being taken seriously, says the BBC's Jonah Fisher in Johannesburg.
A march planned for Monday was cancelled and the message sent out to party members, not to create trouble, our correspondent says.
The first test of this apparent cooling of emotions will come on Tuesday when the two young men accused of murdering Mr Terreblanche appear in court, he adds. The AWB has said its members will attend peacefully.
Police say that two of Mr Terreblanche's farm workers have admitted killing the leader of the AWB party in a pay dispute.
Earlier on Monday, South African leaders visited the Terreblanche family to pay their respects, amid tight security.
North West province Premier Maureen Modiselle passed on the government's sympathies.
TERREBLANCHE: KEY DATES
1941: Born on farm in Transvaal town of Ventersdorp
1973: Co-founds AWB to protect rights of Boers' descendants
1993: AWB vehicle smashes into World Trade Centre in Jo'burg during talks to end apartheid
1994: AWB invades tribal homeland of Bophuthatswana and is defeated; three AWB men die
1998: Accepts moral blame for 1994 bombings that killed 21
2001: Jailed for attempted murder of farm-worker
2004: Released from prison
"As government we are calling for calm and respect of the law, especially here in this region," Ms Modiselle's spokesman, David Sengiwe, quoted her as telling the family.
Mosiuoa Lekota, leader of the opposition Cope party, also visited the Terreblanche family farm.
A veteran of the fight against apartheid, he condemned Mr Malema's singing of the "Shoot the Boer" song.
Following complaints by Afrikaner groups, this was recently banned as hate speech by a South African court, although the ANC says it will appeal.
Boer is Afrikaans for a farmer, but is sometimes used as a disparaging term for any white person in South Africa.
Mr Malema is due to return from Zimbabwe later in the day, and correspondents say his response to calls for calm is keenly awaited.
President Zuma went on television on Sunday to condemn what he said was a "cowardly" murder and a "sad moment" for the country.
Mr Terreblanche was beaten to death in his bed on Saturday evening at his farm near the town of Ventersdorp, North West province. He is due to be buried on Friday.
He had founded the white supremacist AWB in 1973, to oppose what he regarded as the liberal policies of the then-South African government.
His party threatened civil war in the run-up to South Africa's first democratic elections, before sliding into relative obscurity.
Mr Terreblanche served three years in jail after being convicted in 2001 of the attempted murder of a farm worker.