Labor has accused Immigration Minister Peter Dutton of bullying Human Rights Commission president Gillian Triggs, as hostilities between the professor and the government continues.

Shadow Attorney-General Mark Dreyfus told ABC Radio on Monday morning that Professor Triggs was doing her job despite being “bullied” and “vilified” by the government.

The comments came after Mr Dutton launched an attack on Ms Triggs after two speeches she gave last week. The New Daily reported he accused her of linking the execution of the Bali Nine drug smugglers with Australia’s border protection policies.

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“It’s no way for any government to behave and they need to just get an understanding of what’s called for,” Mr Dreyfus told the ABC’s AM program.

“Next we’ll see them attacking judges.”

At a forum in Adelaide last week, Ms Triggs said: “Have we thought about what the consequences are of pushing people back to our neighbours, Indonesia?”

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

The next day, Mr Dutton told reporters in Brisbane the comments were insulting and demanded Ms Triggs retract her statement.

“It is offensive to the government, to the Australian public, but most of all it’s offensive to the families of the two men involved,” he said.

Undeterred, Professor Triggs made another speech that night, criticising the government on several fronts including its plans to remove Australian citizenship from dual nationals involved in terrorism.

“The overreach of executive power is clear in the yet-to-be-defined proposal that those accused of being jihadists fighting against Australian interests will be stripped of their citizenship if they’re potentially dual citizens,” Professor Triggs told a Melbourne audience.

On Sunday, Mr Dutton was asked by reporter Andrew Bolt if he’d like to see Professor Triggs gone.

“When you reduce the position to basically that of a political advocate I think it is very difficult to continue on,” he told Ten Network’s The Bolt Report.

He said her appointment was a matter for Attorney-General George Brandis.

“These are issues for Professor Triggs to contemplate,” Mr Dutton said.