Attorney-General George Brandis has continued the Federal Government's condemnation of Human Rights Commission president Gillian Triggs, repeating that he has "lost confidence" in her.

The Government has accused Professor Triggs of linking asylum boat turn-backs to Indonesia's lack of engagement on the death penalty, a claim she denies.

"Is it any wonder that Indonesia will not engage with us on other issues that we care about, like the death penalty?" she asked.

Senator Brandis said she was wrongly connecting asylum policy to the executions of Bali Nine pair Andrew Chan and Myuran Sukumaran.

"The position is, I'm sorry to say, that the Government has lost confidence in Professor Triggs. I say that with some regret because I personally like Professor Triggs and it saddens me to say this," he told the ABC's AM program.

"She talked about Australia's engagement with Indonesia on the question of the death penalty.

"The main conversation in this country about the death penalty in Indonesia in recent months, as we all know, had to do with the execution of Chan and Sukumaran.

"To link Australia's turn-back policy to our capacity to engage with Indonesia on death penalty issues was plainly wrong."

The Federal Government earlier this year said it had lost confidence in the human rights boss after Professor Triggs released the Forgotten Children report about children in detention.

The Government slammed her for not launching the inquiry under the previous government.

"The Human Rights Commission, in my view, is an important national institution, but it has to be like Caesar's wife, it must both be and be seen to be above partisan politics," Senator Brandis said.

"Professor Triggs's decision to delay holding an inquiry into the issue of children in detention — all of whom were put into detention by a Labor government until after the Labor Party had left office — can only be interpreted and has been interpreted by many, many people in Australia as an act that looked partisan."

Race Discrimination Commissioner Tim Soutphommasane defended his colleague.

Sorry, this video has expired Tim Soutphommasane defends Gillian Triggs

"I support Gillian Triggs in her role as president and we do our job at the Human Rights Commission without fear or favour," he told ABC News Breakfast.

"What we say won't always be agreeable to governments, but it's part of our job as the national human rights watchdog to call it as it is.

"We make our interventions in public debate based on evidence and research and based on our obligations under statute and under international law — and that's what Professor Gillian Triggs has done."