Labor has complained that the attorney general, George Brandis, “inappropriately” insisted his staff “oversee” a meeting between the human rights commissioner, Gillian Triggs, and the opposition.

The shadow attorney general, Mark Dreyfus, told Guardian Australia he had complained to Brandis after the attorney general instructed his staff member be present when Dreyfus met Triggs late last year, not long after the commission delivered to government its final report on children in detention. The meeting was not about the report.

Triggs had informed Brandis that Dreyfus had asked to meet her as a “usual courtesy”. When Brandis’s deputy chief of staff, Josh Faulks, turned up at the commission’s Sydney office at the appointed time for the meeting, both Dreyfus and Triggs asked him to leave. Faulks refused, saying he was acting on the instructions of the attorney. The meeting proceeded with Faulks watching.

“Independent statutory agencies ought to be free to consult with anyone in Australia, including the opposition, without being supervised or overseen by a ministerial adviser,” Dreyfus told Guardian Australia.

“It is appropriate for ministerial advisers to be present at security briefings provided to the opposition, or when the opposition is receiving a briefing from a government department, but it is not appropriate for ministerial advisers to oversee meetings with an independent statutory agency.”

While it is demanding that staffers sit in on meetings between Triggs and the opposition, the government is refusing to meet her. Guardian Australia understands the prime minister, Tony Abbott, has refused requests for meetings, and Brandis has been unable to find time in recent months.

Sources said there was no record of any government insisting on a staff member sitting in on a meeting between the opposition and the human rights commission.

Abbott has attacked the commission and Triggs for the children in detention report which criticised the impact on children of the detention policies of both the Coalition and Labor. Abbott described it as a “transparent stitch-up” and a “blatantly partisan exercise”. Earlier this year Brandis sent the secretary of his department, Chris Moraitis, to suggest Triggs stand down from her five-year stint as commission president. During that conversation she was offered another position.

Government backbenchers have also made increasing numbers of public calls for Triggs’s resignation and threatened a parliamentary inquiry into “bias” in her organisation.

But the UN’s working group on arbitrary detention has defended Triggs’s “high reputation” and the “reliable” findings of the report, and urged the government to “respect the rule of law”.

Australia’s peak law bodies and academics have also backed Triggs, warning that attacks on her by the government are a threat to democracy.

Brandis was asked about the meeting a week after it occurred, during Senate estimates hearings late last year, and said it was routine for a staff member to be present.

“I did require a member of my staff to be present. That was routinely – routinely – required of me when I was in opposition when I was briefed as the shadow attorney general by various agencies of the executive government.

“… Ordinarily the opposition, in my view, ought to expect to be able to be briefed about the operation of an agency by the CEO of the agency. But ordinarily the minister, or a representative of the minister, would sit in.”

He said ministerial advisers always sat in on the legally required briefings to oppositions from Asio, and that made it all the more obvious that they should sit in on briefings provided not as a legal requirement, but as a courtesy.

“If a member of the staff of the attorney general should sit in on a briefing where there is a statutory right, then a fortiori the member of the staff of the attorney general ought to sit in on a briefing which is given as a matter of convention or perhaps as a matter of courtesy. That was done, and I am told that my deputy chief of staff, Mr Josh Faulks, did sit in on that briefing and he did not in any way, shape or form seek to interfere with the conversation. He was merely present, as is appropriate.”

Triggs is due to give evidence to a Senate estimates committee next week.