Peris says she accepts an apology from Nelson and considers it to be “genuine and remorseful”, she wrote on Twitter.
“I hope he reconciles [with] his family,” she said.
In his apology, dated 5 July, Nelson said his Facebook post on 28 May brought “far reaching consequences to Ms Peris, the indigenous community, the Australian people and shame to myself and my family”.
“My outburst of malicious foul language is inexcusable and on reflection I cannot believe that I was responsible. I cannot explain my action.”
Nelson pleaded guilty in June to one count of using a carriage service to offend and was handed an eight-month suspended sentence.
He was arrested and charged in late May over a comment on the former Northern Territory senator’s Facebook page that told her to “go back to the bush and suck on witchity grubs and yams”.
The post also said that Peris was “only endorsed by Juliar [Julia Gillard] because [she was] black”, and criticised her for wearing white ochre on her face during her 2013 maiden speech.
Peris shared a screenshot of the offensive post on her Facebook page on 28 May with the comment: “#Racism – it stops with me.”
“I’ll continue to wear ochre on my face just like my people have done for thousands of years! My skin is my pride,” she wrote in a comment responding to Nelson.
“P.S. Never had a witchy grub. I’m coastal, the mangrove worms are delicious & the yams are amazing.” She concluded her comment with a peace-sign emoji.
Peris was hand-picked by then prime minister Julia Gillard in 2013 to become the first Indigenous woman to be elected to Australia’s federal parliament.
Nelson had been the secretary of the Woy Woy branch of the Liberal party until he was expelled from the party after the allegations were first made.
He initially claimed he had been “the victim of a really horrible and extremely vicious hacking”.
“I’m definitely not a racist,” he told the Central Coast Gosford Express Advocate last month. “I’ve got friends who are Aboriginal and family who are Aboriginal.”
He said he had received death threats as a result of the publicity, and his business name had been “trashed by the online haters”, potentially fast-tracking his plans to retire.