Michaela Banerji was working in the communications area of the Department of Immigration and Citizenship when she posted several tweets on her private Twitter account, which had about 700 followers.

The tweets were critical of the government and the opposition, the department and its spokesman, Sandi Logan, and a company contracted to run immigration detention centres.

She was dismissed by the department on September 13, with her last day on September 27.

The government argued she had breached the Australian Public Service's code of conduct, which states employees must avoid making "harsh or extreme" criticisms of politicians or policies.

The sacking sparked a legal battle, with Ms Banerji turning to the courts in an attempt to save her job.

But she lost three different applications to have a stay on her dismissal, the last of which was rejected in the Federal Court in late September.

That last-gasp bid in the Federal Court was designed to temporarily keep her job until her appeal could be heard in October.

Ms Banerji appeared before the Federal Court again on Wednesday.

The former public servant, who has legal training and is representing herself, said there was mutual agreement for her to discontinue her appeal.

Instead, she is taking the matter to the Fair Work Commission, where she will seek to fight against her unlawful dismissal.

A conference is expected to take place before the Commission in November.