More than 40,000 people have joined a petition asking that a family of Tamil asylum seekers, summarily detained by the Australian Border Force, be allowed to remain in Australia.

The Guardian reported on Monday on the detention of Nadesalingam and Priya, and their Australian-born daughters, nine-month-old Dharuniga and two-year-old Kopiga, who were forcibly taken in a dawn raid on their home in the Queensland town of Biloela, on 5 March, over a visa expired by a single day.

A change.org petition started by Biloela social worker Angela Fredericks has asked the Department of Home Affairs to reassess the family’s claim for protection, in view of mistreatment of Tamils involuntarily sent back to Sri Lanka.

A week since the raid, the family remains in immigration detention more than 1,500km from their home, awaiting possible deportation.

They have described their detention as “like house arrest” with guards posted outside their door and limited time, as little as half an hour a day, for their children to play outside.

The petition – which went from a dozen signatures to more than 40,000 in just over 24 hours – argues the family has made a home and life in Australia, and has become a valued and loved part of the community.

“Our community is not ready to let this family go,” Fredericks wrote. “They love living and contributing to our society. We want them here. Mr Dutton, please return this family to Biloela, their home.”

The Queensland Greens senator Andrew Bartlett said the family was “integrating and contributing to their community in precisely the way the federal government says migrants should”.

He said they had faced “traumatic treatment” at the direction of Home Affairs.

The UN has reported that Tamils, particularly those with links to the now-defeated separatist army, the Liberation Tigers of Tamil Eelam (the LTTE or Tamil Tigers), face systematic persecution and torture. Like many Tamils in the north, Nadesalingam had links to the LTTE.

Last month Amnesty International reported the Human Rights Commission of Sri Lanka continued to document widespread incidents of violence against detainees.

But a spokesperson for the Department of Home Affairs said the family’s asylum application had “been comprehensively assessed by the department, various tribunals and courts”.

“They have consistently been found not to meet Australia’s protection obligations.

“Foreign nationals who do not hold a valid visa and who have exhausted all outstanding avenues to remain in Australia are expected to depart voluntarily.

“All detention and removal operations are carried out in a way that ensures the safety and security of detainees. Appropriate consideration is given to the needs of any children involved.”

Much of the controversy has been over the manner of their detention and the treatment of their children.

Australian Border Force officials, accompanied by police and Serco guards, arrived at the family’s home at 5am on Monday. The family said they were given 10 minutes to pack before being flown to Melbourne.

There, they said, they were told to sign documents assenting to “voluntary removal” and told that, if they did not sign them, they would be denied access to a phone and forcibly deported separately.

On Tuesday afternoon they signed the papers but said it was under unfair duress.

The family had been living in Biloela for four years, where Nadesalingam worked at the meatworks. Nadesalingam and Priya married in 2014, having arrived separately in Australia by boat seeking asylum in 2012 and 2013, in the aftermath of Sri Lanka’s 26-year civil war.

Nadesalingam’s application for protection has been rejected by Australia and his appeal options extinguished.

Legal avenues remain over Priya’s bridging visa. It expired on 4 March but she was in regular communication with Home Affairs officials beforehand to have it renewed. She said she had been told she would be receiving a new visa by mail.

The Sri Lankan government has consistently denied mistreatment of Tamils is occurring. “Come back. All is forgiven,” the Sri Lankan prime minister, Ranil Wickremesinghe, said when he visited Australia in February last year.