Sosefo Kauvaka Lelei Tu'uta Katoa, 29, is now set to be banished to his native New Zealand after all seven judges of Australia's top court ended his three-year fight to stay.

The former Canberra Comanchero sergeant-at-arms was behind bars on remand, facing charges that included bomb possession and blackmail, when then-immigration minister David Coleman cancelled his temporary visa on character grounds in September 2019.

On the day of the minister's decision, the ACT Magistrates Court heard police also suspected Tu'uta Katoa of involvement in up to 61 gang-related shooting or arson attacks.

Tu'uta Katoa, who was subsequently transferred to immigration detention on Christmas Island, had five weeks to apply to the Federal Court for judicial review of the decision.

He missed the deadline by about three weeks, meaning his lawyers had to seek Justice John Nicholas' leave for an extension of time in which to appeal.

They proposed to argue that Mr Coleman had acted contrary to the presumption of innocence by taking into account by taking into account unproven allegations when he concluded that Tu'uta Katoa posed a risk of reoffending.

Justice Nicholas dismissed the application last August, noting the minister had also looked at Tu'uta Katoa's proven criminal history and ascent to the senior rank of sergeant-at-arms.

"The minister found that [Tu'uta Katoa's] membership of the Comanchero OMCG heightened the risk of harm [he] posed to the community and that his conduct as a member of the Comanchero OMCG demonstrated a lack of respect for law and order in Australia," Justice Nicholas said.

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Tu'uta Katoa later made a successful application for special leave to appeal against Justice Nicholas' decision in the High Court, which heard his case in May.

His lawyers claimed Justice Nicholas had "committed jurisdictional error", arguing the Federal Court judge had assessed the application for an extension of time on the basis of "full argument" rather than on "an impressionistic basis".

The High Court dismissed the argument on Wednesday, finding it was appropriate for the Federal Court to "engage in more than an impressionistic assessment" in some cases.

"It was permissible, and in this case appropriate, for [Justice Nicholas] to assess whether the proposed ground of appeal had any merit in order to decide the extension of time application," a judgment summary says.

The decision means Tu'uta Katoa, who has complained in New Zealand television interviews and on a true crime podcast about the conditions on Christmas Island, has now exhausted all avenues in his protracted fight to avoid being booted out of Australia.

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