"Our clients are relieved that three family members have had their bridging visas extended by a year today - this is a step in the right direction," Carina Ford said on Twitter.
"To make it clear, the Minister has chosen not to use his public interest power to release the youngest child from community detention, meaning the family cannot return to Bilo and will remain in Perth."
The decision comes a week after the family was granted a reprieve in its fight to remain in Australia after a three-month bridging visa was granted, which had allowed them to stay in the country until just before Christmas.
Minister Hawke's office said it would not be providing a statement.
The family has been living in Perth after being released from years of detention - the last stint on Christmas Island - after Tharnicaa was medically evacuated from the island earlier this year with a blood infection that left her gravely ill.
The family’s supporters say they are “surprised” by Minister Hawke's decision to now grant 12-month visas to three of the four family members, while continuing to withhold a bridging visa for Tharnicaa.
Angela Fredericks, Biloela resident and a family friend, told SBS News while the decision brings a "huge amount of joy" to the family, it doesn't offer any permanency.
"For the family, we don't get too many wins. So this is a huge amount of joy for Priya and Nades today, and I really want them to enjoy that," she said.
"There is still the unknown as to what is going to happen with little Tharnicaa."
Labor's home affairs spokesperson, Kristina Keneally, described the decision as "unfair".
"With the stroke of a pen, Alex Hawke could've simply let the Biloela family go home to Bilo. He has the power!" she wrote on Twitter.
"Twelve-month bridging visas is good news, but using Tharni to keep them in Perth - 4,500 kilometres from Bilo - is unfair."
The Murugappans were living in Biloela before Priya and Nades' bridging visas expired in 2018, after which the family was taken into detention during a night raid.
Nades and Priya have said they face persecution if deported to Sri Lanka. They fled their homeland after the country's civil war and came separately by boat to Australia.
The government has repeatedly said the family is not eligible to permanently settle in Australia.
'We are still going to keep fighting'
Ms Fredericks said the family has been able to enjoy a "normal existence" while in Perth, where Nades has returned to work as a cleaner.
"It has brought him so much joy to be able to provide for his family once again," she said.
She said Kopika is going to school, while Tharnicaa is in kindergarten.
"They love learning, they are the brightest little girls. On the weekend, it’s about them being able to go to the park," she said.
"Priya has people over and cooks meals for them. So, they are able to just actually have a normal existence ... However they still don't have complete freedom."
Ms Fredericks said the family's supporters "are still going to keep fighting".
"Until we have all four members on visas, we are not going to relax."