Predrag Japranin is the second Australian man to be accused of war crimes during the 1990s war in Croatia.
He was placed on Interpol's "most wanted" list at Croatia's request in 2012.
Predrag Japranin's father, Djuro - also based in Melbourne - says his son was a soldier in the Yugoslav National Army during the Croatian conflict.
But he says he didn't hear until this week about the allegations against him and he doesn't believe they could be true.
"If he had committed such crimes my wife and I wouldn't have returned to Croatia five or six times, rebuilt our home, and we wouldn't have the intention of returning to live there," he told SBS.
"I don't know where the information that he has killed civilians has come from. I don't believe it."
SBS reporter Kristina Kukolja reports
Djuro Japranin's father says Predrag has been advised by his lawyer not to give media interviews.
The Australian Federal Police says that unless Croatia makes a formal extradition request, it does not have the power to arrest Predrag Japranin under the terms of an Interpol Red Notice.
"The AFP advised Interpol Zagreb that it believed Pedrag Japrinin was in Australia," a spokesperson for the AFP said. "Future action in this matter would be for Croatian authorities to progress formal extradition proceedings."
Croatia has confirmed to SBS it will not consider any further war crimes extraditions from Australia until a final decision is made in the case of Daniel Snedden.
Croatia's Justice Ministry said it believes the Snedden case will set a legal precedent.
"Such a decision will be a precedent which will indicate Australia's final stance about the extradition of its citizens," the department said.
"In line with the above and on the basis of the decision of the responsible judicial bodies in Australia about the extradition of Dragan Vasiljkovic, the final position of Australia towards the extradition of its citizens will become apparent, and on the basis of it, the Republic of Croatia will request the extradition of Predrag Japranin."
Daniel Snedden, also known as Dragan Vasiljkovic or Captain Dragan, is wanted by Croatia over alleged war crimes in the 1990s.
The Australian citizen, who was born in Belgrade, has spent several years in jail in Australia after Croatian authorities requested his extradition in January 2006.
Croatian court documents allege he ordered the killing of prisoners of war and led an assault on a village in which civilians were killed during the 1990s Balkan war.
Mr Snedden has been fighting extradition to Croatia in Australian courts since 2007.
In its first year of EU membership, Croatia has extradited 75 people to EU countries and 33 people to Croatia, the Croatian Times reported.
The extraditions were for criminal prosecution cases and enforcement of jail sentences for crimes including murder, rape and fraud.
The Attorney-General's department said it would not publicly comment on the case of Predrag Japranin unless an arrest is made or the matter is brought before the courts.
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