Priya and Nadesalingam and their two Australian-born children

The federal government has been ordered to halt the deportation of two members of a Tamil family as they await an appeal about whether they can return to the country Queensland town they call home.

Priya, her husband Nadesalingam and the couple's two children are being held in immigration detention in Melbourne.

On Monday, Federal Court Justice Bernard Murphy granted an urgent injunction prohibiting immigration authorities from deporting Priya and her three-year-old daughter.

Priya was issued with a deportation notice on Friday, a day after losing a bid to stop the family's deportation at the Federal Circuit Court.