His statement comes a week after he scooped the £10,000 ($13,000) award and a recent article in The Atlantic said AI-detection software Pangram had shown his work about a boy whose family falls on hard times was entirely AI generated.
"For the avoidance of doubt, I wrote The Blue Fighter," he posted on X, external.
The accusation has caused an uproar on social media and Caine Prize chair Ellah Wakatama told the BBC she was shocked that the US magazine had not waited for a full investigation before publishing.
"I do wish The Atlantic had spent more time investigating this so that alongside Pangram, they did have evidence of real human investigation of it before tainting the prize and tainting this winner," Wakatama told the BBC's Front Row programme.
The chair of the Caine Prize's board of trustees said she had been contacted on Friday about the allegation and Vauhini Vara's article - Yet Another Prizewinner Seems to Be AI, external - had been published on Sunday.
Vara, who quoted Wakatama in her article, said her wariness of Silicon Valley was "well founded and reasonable" but she said Pangram's internal research showed its assessments were rarely wrong.
Zimbabwean writer Joe Ruzvidzo, whose novel Welcome to Anywhere came out last year, said he stood by Kundizeza and that it was time "to fight this literary stop-and-frisk", external.
Nigerian publisher Modupe Daramola said it was necessary to discuss how "these AI allegations are targeting Black and African writers" and how they were often disproportionately scrutinised.
"There's something incredibly sinister about this," the Noisy Streetss Limited publisher posted on X, external.
Wakatama said as part of an internal investigation for the Caine Prize Kundizeza would be sending in documentation about his various drafts and there were ongoing conversations with all the judges and The Shallow Tales Review, the publication that first published The Blue Fighter in 2025, external.
In his statement, Kundizeza said had "a concrete, documented history" about the story's inspiration and he set out the chronology of its development.
Wakatama, who is also editor-at-large at Canongate Books, said Caine Prize submissions, which are all previously published, were not checked for AI, but writers vouched that their work was original.
Wakatama said it was also important to remember Pangram was "not yet tested".
In her article, as well as citing Pangram research she also quoted a recent paper by researchers at Free University of Brussels, external, which said it had found zero cases of Pangram, and two other AI-detection tools, getting it wrong when it came to English-language writing by non-native English speakers.
Vara told BBC's Front Row programme that she had also used her own judgment "to suss out these things" and that every other previous Caine Prize winning story she had put through Pangram "came out as 100% human".
"The proliferation of those struck me," Vara told Front Row, adding that the story also had a lot of metaphors, also prevalent in writing generated by AI.
The day after winning the Caine Prize, Kundizeza told the BBC he was inspired after hearing a poem read by South African Vangile Gantsho at an event in Ghana last year about her father's obsession with building fish tanks.
So it kind of touches on both of our fathers," he told BBC Newsday.
On X, Kundizeza said he was heartened by "the numerous messages of solidarity from fellow writers and readers", ending his message by saying: "Most importantly, I will continue to write."