The Senate has censured Attorney-General George Brandis, saying he is “unfit to hold the office”, over his behaviour in relation to Human Rights Commission President Gillian Triggs.

The motion, moved by the opposition and carried 35-32, condemned Brandis for failing to defend Triggs from “malicious attacks” and seeking to get her to resign by “facilitating an offer of an alternative role”.

Apart from the opposition and the Greens, Clive Palmer’s two PUP senators voted for the censure and so did ex-PUP and now independent senator Jacqui Lambie. Independent Nick Xenophon voted against, as did Family First senator Bob Day.

The vote has no practical force and is only possible because the government is in a minority in the Senate. Nevertheless the upper house relatively rarely uses its numbers to carry such a serious motion.

Moving the censure, Labor’s Senate leader Penny Wong said the government’s reaction to the commission’s report, The Forgotten Children, gave an insight into the psyche of a dysfunctional government, which was “permeated by bullying and cowardice”, notably from “bully-in-chief” Tony Abbott and his lieutenant Brandis.

The commission had criticised the policies of both Labor and Liberal governments, she said. “Yet never before has a government reacted to this criticism so viciously and so personally.

"The attorney-general has failed to defend the commission from political attacks, he has attacked the independence of the commission, he has tried to force the president into resigning, he has sought to procure that resignation by offering an alternative position and he has placed the secretary of his department [who was sent to tell Triggs she had lost the confidence of Brandis] in an invidious position,” Wong said.

“He has not only displayed a lack of integrity, he has behaved in a cowardly fashion.”

Brandis repeated that Triggs had lost his confidence and the confidence of the non-Labor side.

The genesis of the loss of his confidence had been the November Senate estimates committee hearings, “when Professor Triggs, given numerous opportunities to do so, was unable to explain why it was that the holding of the inquiry into children in immigration detention was delayed so that it did not commence before the 2013 election”.

Triggs had cost the commission its reputation for bipartisanship, Brandis said. He denied there had been malicious attacks on her. He had “a high personal regard” for her and was particularly conscious of her reputation as an eminent international lawyer. But “just because a person might be a distinguished academic, it does not mean they necessarily have the skills to manage an agency of the executive government”.

The public was entitled to know the reasons the government had lost confidence in Triggs, Brandis said. He had given an account of the reasons and “to say that is not to attack her character or to be a bully boy – it is merely to explain why a particular conclusion has been reached”.

Brandis said the commission was not a court that should not be criticised. It “must deal in controversial contemporary public affairs … it should never be above criticism”.

Lambie said that “you cannot support Professor Triggs and not support this censure motion. It is either one position or the other”. The attacks by Abbott and Brandis on the president had been “vicious and extraordinary”.

Lambie praised the government for securing Australia’s borders, stopping mass drownings and putting people smugglers out of business.

“However, the good the Liberals did for Australia’s border protection and national security is overshadowed by the vindictive, personal attacks” by Brandis and Abbott on Triggs, Lambie said.

“We all know that the political attack on Professor Triggs was supposed to somehow appeal to the base of the Liberal Party – and was really designed to boost Tony Abbott’s leadership stocks.”

Xenophon criticised Brandis for not defending Triggs but said he did not think the minister was unfit to hold the office.

In question time, the prime minister continued his attack on Triggs.