The family of a Tongan man who plunged to his death at Melbourne's Maribyrnong Detention Centre has started legal action against the Federal Government of Australia.

Viliami Tanginoa, 53, spent more than eight hours up a basketball post before falling to his death on the day he was to be deported to Tonga five years ago.

Two years ago a Melbourne coroner found the management of the detention centre contributed to the death of the detainee.

The family's lawyer, Dina Tutungi, says the family is also seeking damages from the former operator of the centre, Australasian Correctional Management.

"The family are seeking compensation for the distress and trauma and suffering that they have sustained as a result of this tragic situation and death," she said.

Ms Tutungi says the family has commenced the first legal case claiming the wrongful death of a detainee on behalf of his family in the County Court of Victoria. - ABC