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Hubbard will become the first transgender athlete to compete at the Games after she was selected by New Zealand's Olympics committee in the women's super-heavyweight 87+ kg category.
"Parties here have simply followed the rules. That's the case for Laurel but also the team in New Zealand - they have followed the rules," Ardern told reporters in Wellington on Tuesday.
"The alternative is to have someone who followed the rules but then is denied the ability to participate," she said.
"So, ultimately, I leave it to those bodies and that's the decision they have made and it's in keeping with the standard that has been set globally."
Hubbard, who at 43 will be the oldest lifter at the Games, had competed in men's weightlifting competitions before transitioning in 2013.
She became eligible to compete at the Olympics as a woman when the International Olympic Committee (IOC) issued guidelines in late 2015 allowing any transgender athlete to do so, provided their testosterone levels were below 10 nanomoles per litre for at least 12 months before their first competition.
Revisions by the International Weightlifting Federation in May this year to its qualifying requirements - reducing the number of events contenders needed to participate in - put her in the frame for selection.
Some scientists have said the revised IOC guidelines on gender participation do little to mitigate the biological advantages of those who have gone through puberty as males.