David Farley, who is in his second sitting week in parliament, voted on Tuesday with the teals and Greens to cap the fuel tax credit scheme for the most profitable mining companies.
Labor and the coalition opposed the amendment, which was defeated.
Mr Farley realised he had made a mistake due to his "inexperience in parliament" and tried to change his vote, but was unable to, he said in a statement on Wednesday night.
"I reiterate I completely support all of One Nation's positions and policies. I would not be a member of the party otherwise," he said.
"There is no policy or position difference between me and One Nation leader Senator Pauline Hanson, who has my full support. I am privileged to have her support as well."
Mr Farley was elected as the MP for Farrer in a by-election in May following the resignation of former Liberal Party leader Sussan Ley.
He also blamed his voting error on the Labor government's "refusal" to grant One Nation funding for more advisors, saying the team was "significantly overworked".
"Recruiting experienced staff to support my work has been difficult, however I am rectifying the situation," he said.
While the allocation of staff is at the discretion of the prime minister, it generally relies on well-established conventions detailing the level of funding each party is given.
Mr Farley was asked on Tuesday if he voted with the teals because he was caught out by the speed of the process, to which he said "no".
But his mistake has led to blowback from industry groups, including the Minerals Council.
Chief executive Tania Constable said he had voted against many of his constituents.
"He voted against the farmers, the fishers, the construction industry. He voted against the miners. He voted against regional Australia and we're really deeply disappointed that he threw his lot in with the Greens and the teals," she told Sky News.
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