Archbishop Desmond Tutu has said that Nelson Mandela would have been appalled that Afrikaners were excluded from memorial services marking his death.
He highlighted the absence of the Dutch Reformed Church and the limited use of the Afrikaans language at the services.
A mainly Afrikaner party introduced white minority rule, which Mr Mandela opposed, spending 27 years in jail.
But after becoming South Africa's first black president, Mr Mandela preached reconciliation with his former enemies.
Archbishop Tutu also strongly criticised the prominence of the governing African National Congress (ANC) during the week of events following Mr Mandela's death on 5 December.
"I also believe it may have sent out a more inclusive message had the programme directors at the Memorial and Funeral - both national and State events - not both been senior office-bearers of the ruling party," he said.
Archbishop Tutu fought apartheid, along with Mr Mandela and the ANC, but has become increasingly critical of the party, recently saying he would vote for the opposition.
He almost did not attend Sunday's funeral for his close friend, saying he had not been invited.
In a statement, he described Mr Mandela as a "nation builder" who "went out of his way" to include Afrikaners after the end of apartheid.
"We were amiss in not being as inclusive as Madiba [Mandela's clan name] would certainly have been," he said.
"To the extent that I can do so meaningfully, I apologise to our sisters and brothers in the Afrikaner Community," he added.
Archbishop Tutu said non-members of the ANC hierarchy should have been allowed a greater role in the organisation of the services
Archbishop Tutu said Mr Mandela's belief in reconciliation was evident in the composition of the new national anthem, which has a verse in Afrikaans, and his involvement in "the 1995 Rugby World Cup, the lunch and tea engagements with the widows of apartheid presidents."
Rugby was closely associated with Afrikaners and Mr Mandela's decision to wear the national team shirt in 1995 won him great respect in the community.
"Madiba was a nation-builder. I pray that we will uphold this critical aspect of his mission forever," the archbishop concluded.
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