"I call on everybody, but especially the brothers and sisters from the Afrikaans-speaking community... if you please just confess and repent people will be prepared to forgive you.
"Almost everydody who has testified before us is not looking for revenge. They simply want to know the truth."
Speaking on the first day of the commission's Durban hearing, Tutu said Afrikaners could make a "huge contribution" to national reconciliation and healing.
"When an Afrikaner sees the light, nothing can hold him back. He gives of his best."
He said the commission could not be accused of bias or of being a witchhunt as it had striven to hear cases from across the political spectrum.
He again stressed that alleged perpetrators of human rights abuses would be given "reasonable and timeous notice" of the commission's intention to hear evidence implicating them in apartheid-era crimes.
Those named would be entitled to tell their side of the story and to conduct limited cross-examination of their accusers.