After reports that the heads of the three federal courts would meet in the next two weeks to discuss structural changes, shadow attorney-general Mark Dreyfus said the government could not be trusted with the reform.

"Senator Brandis has so far said absolutely nothing about what his plans are," he said.

"Prime Minister Turnbull must demand that Senator Brandis publicly detail his plans for the Family Court, and do so straight away."

The reports came as the Federal Court remained locked in a workplace dispute with staff, who say their bosses haven't listened to their fears about cuts to rights and conditions in a proposed enterprise agreement.

Workers at the Federal, Family and Federal Circuit courts and National Native Title Tribunal went on strike on Friday afternoon, while earlier that day their employers refused conciliation by the Fair Work Commission.

At a swearing-in of the new chief justice of the Family Court and the chief judge of the Federal Circuit Court on Friday, Senator Brandis said the government would work with the judges to consider structural improvements to the courts.

"The renewal in the leadership of these courts gives us a rare opportunity to consider afresh their structure and operation," he said.

"The government will work with the two new heads of jurisdiction, as well with the chief justice of the Federal Court, to consider what, if any, structural improvements can be made to the federal judiciary to ensure that Australians who come before the courts with family law matters get swifter, less expensive justice in an environment that seeks to minimise confrontation and enhance the opportunities for consensual resolution of disputes," he said.

"I want to stress that I have an entirely open mind as to what structural reforms are desirable and I will be guided by the views of the heads of jurisdiction, and I look to their leadership in that regard.

"However, we all know that the system is capable of improvement and the government is open to change, if need be, radical change."

Community and Public Sector Union secretary Nadine Flood said the added uncertainty of a merger was the last thing the courts needed, given the industrial dispute.

"Senator Brandis would have been better off meeting with courts employees on Friday as they went on strike for the first time ever," she said.

Ms Flood said management's rejection of conciliation was "a bitter irony" considering that mediation was a principle of the courts' operation.

A Federal Court spokesman said it was continuing to negotiate the workplace agreement and another meeting was scheduled for Wednesday.

"In these circumstances it is considered unnecessary to enter into conciliation at this point," he said.

"We are doing all we can to put the best offer to staff."

Staff are negotiating a single agreement after the Federal Court of Australia's merger of administration with the Family Court and Federal Circuit Court in 2016.

The Federal Court's public servants responded with a 90 per cent 'no' vote in June to a proposal offering them half the wage rises being paid to their counterparts in other departments and agencies.

The courts staff were asked to accept a new deal that offered an average pay rise of 1 per cent for each of the proposed agreement's three years, cuts to conditions and entitlements and, for some, a longer working week.