Australia’s government has been forced into an embarrassing re-vote in parliament after it supported a far-right motion declaring “It’s OK to be white”.

The ruling Liberal-National Coalition blamed an “administrative error” for its senators’ decision to vote in favour of the motion on Monday, which had been put forward by Pauline Hanson, the leader of the anti-immigration One Nation party.

The phrase has been used by far-right groups including the Ku Klux Klan and neo-Nazis to stoke racial division.

On Tuesday, in the face of enormous backlash, the government backed away from its support for the motion, with the prime minister saying the original vote was “regrettable”.

The government accepted a challenge from the opposition Labor party to recommit the vote, with senators present voting unanimously against the motion during the second vote.

The government’s leader in the upper house, Mathias Cormann, said he took personal responsibility for Monday’s error, apologising to the Senate. “This is severely embarrassing,” he told parliament.

After Labor and the Greens cast doubt on the government’s explanation as an administrative error, Cormann said that, while seeming implausible, it was true. “It is often said when wondering whether something is a conspiracy or a stuff-up, go for the stuff-up every time,” he said.

The attorney general, Christian Porter, admitted it was his office’s fault. “An early email advising an approach on the motion went out from my office on this matter without my knowledge,” Porter said in a statement on Tuesday.

“This one was not escalated to me because it was interpreted in my office as a motion opposing racism.

“The associations of the language were not picked up. Had it been raised directly with me those issues would have been identified.”

But the opposition ridiculed the notion that the government did not know what they were endorsing when they supported the motion the first time around. Labor senator Penny Wong said the phrase was used by neo-Nazis and white supremacists.

“Now you want to come in and say, ‘Oops, we made a mistake.’ We don’t believe you. No one believes you, and everybody knows this is a just craven and pathetic attempt to try and clean up your mess,” she told parliament.

Senator Hanson, who declared herself not to be a white supremacist, and fellow conservative crossbenchers didn’t attend the recommitted vote.

“We need to ensure that our white civilisation, our western civilisation, must be protected and looked after,” she told reporters.

The outgoing race discrimination commissioner Tim Soutphommasane, has accused the Coalition government of helping revive race politics as the party fears losing votes on its conservative flank to One Nation.