Hassan Asif, a 25-year-old who came to Australia on a student visa, has been diagnosed with terminal cancer and told he has just weeks to live.
His mother and brother wanted to be with him in his final days, but they were refused visas as they were considered at risk of overstaying.
But the decision sparked an outcry with the Melbourne City Mission homeless refuge, which is caring for Asif, urging Immigration Minister Peter Dutton to "show some compassion".
"Hassan faces a lonely death as immigration department refuse mum's visa," it said on its Facebook page. "We urge Peter Dutton to intervene and reunite Hassan with his family one last time."
The Labor opposition demanded Dutton "sort out this bureaucratic bungle".
"On the face of it, it seems a cruel and callous decision to refuse his Pakistani-based mother and brother a visa to visit Mr Asif," said shadow immigration minister Richard Marles.
"This appears to be a disgraceful and heartless decision."
Dutton, holding a press conference today afternoon, said it was the "right decision" to refuse the visas based on the information that was provided.
But within half an hour he had changed his mind.
"I'd asked the post in Islamabad to have a look at the case, to ask for additional information. That's happened and the visas have been approved," he told Sky News.
"I'm hopeful that they can arrive in Australia soon and spend some time with their terminally ill son and brother. I think that's what most Australians would expect."
Melbourne City Mission's Sherri Bruinhout said Asif cried when he heard the news.
"There were tears all round when his brother called Hassan, the family are thrilled and delighted to be able to come Australia," she told Fairfax Media.
"When we heard the news everyone was crying."
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