Former African National Congress activist Philemon Maxam was jailed for the 1986 murders of widow Ruby Foster, 50, a housekeeper on a Paarl farm, and John Geyser, a 52-year-old casual labourer.
Maxam told the commission he wanted to meet Foster's family so that he could personally apologise for the pain he had caused.
In a letter to the commission, Foster's son, Dr Ivan Sieberts, said: "I am very happy that Maxam wants to make peace, because I too felt the burden of the anger laying heavily on me over the years.
"I called his brother, Pat, last year to my office and told him I wanted to make peace with his family. I have no grudge against him (Maxam)."
Sieberts said Maxam had shot his mother as she went to fetch him a glass of water.
"She was the type of person who wouldn't hold a grudge. So I'm glad that Philemon is doing this for her and for me. I think my mother would have wanted it this way."
According to newspaper reports Foster was shot in the head with a small calibre handgun and died immediately while Geyser was fatally wounded.
A number of household items were stolen, including a video recorder.
Maxam, an inmate at Allandale prison, testified that at the time of the murders he had been responsible for implementing the ANC's "M-Plan" in Mbekweni, a township neighbouring Paarl.
"My role was to set up teams of young activists to work on certain strategies to destroy what we saw as the apartheid apparatus. We had to protect ourselves. We needed arms."
He said he had not applied for amnesty for the murders, for which he originally received two death sentences, and was eligible for parole only in 2004.
"I am prepared to serve my whole sentence. It is not that I want to be released through amnesty. I am committed to my responsibilities in prison."
Commissioner Denzil Potgieter said Maxam could be eligible for amnesty if the murders were committed, as he claimed, in a political context.