A Tamil family fighting to stay in Australia have won a two-day reprieve as lawyers battle an overnight decision by the minister not to allow a visa application to be made.

The Federal Court in Melbourne on Wednesday extended the latest injunction protecting the family's youngest child, Tharunicaa, 2, from being deported.

Justice Mordecai Bromberg ordered the Australian government be restrained from forcibly removing the girl until 4pm on Friday.

The court application only applies to Tharunicaa but her lawyers have been assured the family will not be separated.

Tharunicaa, her parents Priya and Nadesalingam and her four-year-old sister Kopika, are detained on Christmas Island as they await the outcome of a last-ditch bid to stay.