Puneet was a 19-year-old learner driver in October 2008 when he hit and killed 19-year-old nursing student Dean Hofstee and seriously injured 20-year-old Clancy Coker in Melbourne.
He was on bail and awaiting sentence after pleading guilty to culpable driving when he fled Australia in 2009 using a friend's passport and hid for more than four years until his capture.
At the latest hearing in the Patiala District Court in Delhi on Monday, Puneet made a plea to the victims' families for forgiveness.
But acting Premier James Merlino says he must return to Australia, saying, "The expectation of the Victorian community is that this individual is extradited to face justice in Australian courts. That's been the consistent position of the Victorian government. The premier Daniel Andrews will be visiting India next week. He'll be conveying this directly to the Indian government. This individual must face justice and he must face justice in Australia."
Puneet Puneet is expected to reappear in the New Delhi court on February 2, for the next hearing.