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Refugee supporters in Melbourne have rallied four times in less than a week in support of Tamil refugees Priya and Nades, and their two Australian-born children, who the government wants to deport to Sri Lanka.

In March last year, the family was raided by police and Border Force officers at their home in Biloela, a small Queensland town where they had lived and worked for four years. They were then taken to a detention centre in Melbourne.

On receiving the news that the family was about to be deported, about 30 people went to Melbourne airport on the night of August 29. 

The family were put on a plane but an injunction prevented their deportation. They were taken to Darwin and then Christmas Island.

Sixty people gathered outside the Federal Court building in the next day, where a hearing was held and the injunction extended to September 4.

On September 1, more than 500 people rallied and marched through the streets of Melbourne. 

Tamil Refugee Council spokesperson Niro Kandasamy spoke at the rally of the physical and psychological damage inflicted on the family in detention, which added to the trauma they had suffered in Sri Lanka.

Kandasamy said that in Sri Lanka, the military occupation of the Tamil homeland continues. Furthermore, the perpetrators of crimes remain in power and run the government. 

She cited UN special rapporteur Ben Emmerson, who said torture is "endemic" in Sri Lanka.

Greens leader Richard di Natale said the government had traumatised the family and that "if [Prime Minister] Scott Morrison is a true Christian he will show compassion".

On September 4, about 100 people rallied outside a Federal Court hearing to determine the families fate. 

Matt Kunkel, from the Victorian Trades Hall Council, said the family are workers and that the union movement will stand by workers wherever they come from. 

Flags from a number of unions were present in the crowd.

Brad Coath, a friend of the family, spoke of the stress the family had been placed under, particularly the children who have now had two birthdays in detention. 

He called on the government to listen to the community and let them stay.

The Federal Court hearing resolved to extend the injunction to September 6.