Government senators have now voted against a motion declaring "it's OK to be white" less than a day after their support for it sparked a humiliating backdown.

Pauline Hanson on Monday brought forward the motion, which also declared "anti-white" racism was on the rise in Australia.

The phrases have been used by far-right groups to stoke racial division.

The original motion was defeated 31-28 despite support from government senators.

The government accepted Labor's Senate leader Penny Wong's challenge to recommit the vote on Tuesday, with senators present voting unanimously against the motion.

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 over the government's explanation as an administrative error, Senator Cormann admitted while seeming implausible, it was true.

"It is often said when wondering when something is a conspiracy or a stuff up, go for the stuff up every time," he said.

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," Senator Hanson told reporters.

Prime Minister Scott Morrison says the government's support was "regrettable" and 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," Mr 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."

Indigenous Affairs Minister Nigel Scullion and his cabinet colleagues Michaelia Cash, Simon Birmingham, Mitch Fifield, Matt Canavan and Bridget McKenzie all voted in favour.

Mr Porter said he was reviewing the processes in his office, which had put government senators in a difficult position because their advice was to vote for the motion.

Senator Cormann said when the One Nation motion first came up in September the government decided to oppose it and instead make a statement saying they deplored racism of any kind.

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.

Victorian senator Derryn Hinch said the government was aware of the motion since September, calling the coalition members "a bloody disgrace".