The family of a dying Pakistani man studying in Melbourne have been granted visas to travel to Australia for a final visit, after their initial application was rejected, sparking a public outcry.

Hassan Asif, 25, has been diagnosed with advanced skin cancer and is too sick to fly home to Pakistan to spend his last days with his mother and brother.  But his dying wish to see his family a final time looked set to be dashed when his mother and brother's initial application to fly to Australia was rejected.

Hassan Asif came to Australia as a student before being diagnosed with terminal cancer. Photo: Facebook

The Department of Immigration said based on the information provided in their application, the pair were considered at risk of overstaying their visa. 

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Mr Asif's plight sparked an outcry in Australia and abroad and the federal government urged his family to reapply for their visa. His family did that in Islamabad on Wednesday morning.

Just before 2pm on Wednesday, Immigration Minister Peter Dutton's spokesman confirmed the family had been granted permission to fly to Australia.

Only minutes earlier Mr Dutton held a press conference, saying while the government stood by its initial decision, he hoped the family would be in a position to travel to Australia "sooner rather than later".

He said with further information and a new application, the issue could be dealt with quickly.

"I've asked for further information to be provided and I think on the basis of that information it's likely that the mother and brother can travel to see their son, their brother here in Australia," Mr Dutton said.

'Tears all round'

Sherri Bruinhout, from Melbourne City Mission, which is providing accommodation and palliative care for Mr Asif, said the student heard the news from his brother.

"There were tears all round when his brother called Hassan, the family are thrilled and delighted to be able to come Australia," Ms Bruinhout told Fairfax Meda.

"When we heard the news everyone was crying, we always had faith that the Australian government and Minister Dutton would see the compassionate side and always knew the Australian public would support it."

Ms Bruinhout said the new visa application lodged on Wednesday included information about the family's finances and support from the local Pakistani community during their stay.

She said it was never Mr Asif's intention to stay in Australia and he had hoped to return to Pakistan and work as an architect.

'Cruel and callous'

Earlier on Wednesday, the federal opposition condemned the initial visa rejection and called on the Minister to explain the "cruel and callous decision."

"This appears to be a disgraceful and heartless decision," Labor's Immigration spokesman Richard Marles said in a statement.

"Mr Dutton needs to immediately intervene and sort out this bureaucratic bungle.

"If there is a legitimate national security risk that should be made clear. Otherwise, commonsense and compassion should prevail."

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