Leorsin Seemanpillai immolated himself on Saturday and died yesterday in a hospital here.
Australian Immigration Minister Scott Morrison said that Seemanpillai "sadly died as a result of a very serious set of injuries that were self-inflicted."
"I don't think we are in any position and I frankly don't think anyone else is any position, to draw any conclusions about what is a person's mind in that situation," he told reporters.
Seemanpillai had arrived in Darwin by boat in January 2013 and was first granted a bridging visa last May. He resided in Geelong after getting the temporary visa.
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Tamil Refugee Council spokesman Aran Mylvaganam said he had known Seemanpillai for 13 months.
He said both his parents lived in a refugee camp in India, and were in shock over their son's death.
"He feared for his life if he was returned to Sri Lanka," Mylvaganam was quoted as saying by the local media.
"His housemates have told me he repeatedly talked about being sent back, he was quite worried about it," he said.
The Sydney Morning Herald quoted Trevor Grant, a convenor at the Tamil Refugee Council, as saying that Seemanpillai "knew that if he was sent back he'd face persecution from the military."
"The immigration officials have been harassing him on many occasions where they wanted him to voluntarily leave," he claimed.
More than 24,000 asylum-seekers are living in Australia on Bridging visas - similar to what was accorded to Seemanpillai.