The 26-year-old freelance reporter, a dual American-British national, was shot in the head during a battle between the South Sudanese army and rebels in the southern town of Kaya on August 26, 2017.
After years of international pressure from the United States and Britain as well as media campaign groups urging a probe into his killing, South Sudan's government announced in October that it would launch an investigation into his death.
The government has repeatedly denied targeting Allen, who had been embedded with rebels from the Sudan People's Liberation Army In Opposition (SPLA-IO) to cover the conflict that erupted just two years after the country declared independence.
On Thursday, David Charles Ali Bilal, head of the investigation committee, told journalists that the attack had taken place around 5:30 am (0330 GMT) and it was very difficult to see "who is black and (who is) white."
"Christopher Allen was unintentionally killed as a result of crossfire," he said, reading out the report.
Allen had "entered South Sudan illegally," he said, adding that he "was not wearing any protective or press identification clothes."
The 2013-2018 war between forces loyal to two sworn enemies, President Salva Kiir and his now deputy Riek Machar, claimed the lives of almost 400,000 people.
The investigation findings reiterated previous claims by South Sudan's government, with Information Minister Michael Makuei saying at the time of his death that "the killing of Christopher Allen was not targeted."
"But anybody on that side is usually a target," the minister added.
Makuei had previously described Allen as a "white rebel" and claimed he had been in the country illegally.
Reporters Without Borders, known by its French acronym RSF, has also been urging the United States to lead a probe into his death because of Juba's "failure to hold anyone accountable."
"Available information demonstrates that war crimes were committed in the deliberate targeting of Allen and the treatment of his body after his death, including trophy-style photos," it said in a statement in August.
South Sudan ranks 118th out of 180 countries on RSF's 2023 World Press Freedom Index and the group says at least nine journalists have been killed in the world's newest nation since 2014.
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