Justice Edwin Wylie tossed out the challenge of the parliamentary process and the validity of the Arms Amendment Act and also dismissed the efforts to prevent the implementation of the law.
He said it was "alarming" to claim that taonga included anything which could deliver a lethal force such as military-style semi-automatic firearms.
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In June last year, the Kiwi Party, which is different to the party of the same name that broke away from United Future in 2007, appealed to the Court of Appeal.
Despite a hearing set to take place on March 3, the party, created by licensed firearms owners, applied last month to "leapfrog" the appeal directly to the Supreme Court.
But Chief Justice Helen Winkelmann and Justices Mark O'Regan and Susan Glazebrook have now dismissed the leapfrog bid and said they were not satisfied there were exceptional circumstances warranting it.
"The Court of Appeal is seized of the matter, the hearing in that court is imminent and it should be permitted to continue the process of dealing with the appeal before it," the judges said in a decision released today.
"In the event that either party seeks leave to appeal to this court against the Court of Appeal's decision, this court can consider the merits or otherwise of granting leave with the benefit of the Court of Appeal's views."
Given the likelihood of a future appeal the Supreme Court justices "refrain from giving any indication of view on the merits of [Kiwi Party's] case".
They ordered the Kiwi Party to pay court costs of $2500 to the Government.
The Kiwi Party's legal counsel, Graeme Minchin, has said the party would fight its case all the way to the Supreme Court if it had enough money to do so.