An epic legal struggle sparked by the alleged racist conduct of a "remarkably unsophisticated" Canberra public servant is set to rumble on after an appeals court found the bureaucrat's ignorance was no defence.

The case, over the use of the words "black babies" and "Coon cheese" to an Indigenous graduate at the Department of Education four years ago is now set to go another round after graduate Edna Vata-Meyer won her appeal this week.

But the full bench of the Federal Court has pleaded with the department and its employee to conciliate the case to avoid more lengthy and expensive litigation.

Without a settlement, the case will return to court with Ms Vata-Meyer suing the department  and eight of its public servants, including department secretary Lisa Paul, and seeking compensation for the racial discrimination allegedly suffered at their hands.

The trouble started in August 2011, seven months after Ms Vata-Meyer moved to Canberra from North Queensland to work at the department, then known as DEEWR, as an Indigenous graduate.

Ms Vata-Meyer said the conduct of her supervisor during a meeting on August 16, later described as a "dressing down", constituted racial discrimination.

Things got worse a month later, on September 28, when co-worker Angus Lee took out a packet of chocolate-flavoured jelly babies, Chicos, and twice offered them to Ms Vata-Meyer and another Aboriginal woman with the words, "Here are some black babies".

At an office afternoon tea later later that day, Mr Lee was asked what sort of cheese he liked and responded, "I just like plain old Coon cheese."

Ms Vata-Meyer complained to her superiors about the comments and Mr Lee, who said he meant no offence by his comments, was counselled and apologised to Ms Vata-Meyer, who then took her complaint about the handling of the incident to Ms Paul.

There were further clashes between the graduate and her superiors that November over her attendance at work, leading to more allegations of racial discrimination, workplace bullying and harassment.

In April 2012, Ms Vata-Meyer wrote to the Australian Human Rights Commission, but the complaint was terminated on the grounds that there was no chance of settlement.

The case then went to Federal Circuit Court, with Ms Vata-Meyer claiming the department, its boss and her public servants, engaged in racial discrimination against her and the Commonwealth was liable for those unlawful acts.

The department and its public servant respondents deny they breached the Racial Discrimination Act and contested some of Ms Vata-Meyer's claims, with the Commonwealth also denying liability.

After court-ordered mediation failed, the case went to a full hearing with Mr Lee giving evidence before Federal Court judge Rolf Driver, saying he meant no offence by his references to black babies or Coon cheese.

The judge gave the bureaucrat the benefit of the doubt "on the basis that he is simply obtuse", and dismissed the case.

But Ms Vata-Meyer appealed the decision, and other aspects of Justice Driver's judgement, to the full bench of the Federal Court with three justices agreeing to set aside the original decision.

The case will be heard again unless the two sides can reach an agreement, as urged by the full bench.

"We would … urge the parties to reduce the burden and expense of a new trial and avoid the uncertainties surrounding its outcome by participating in a mediation," the three judges wrote.