Daniel Andrews on Thursday returned from holiday, a week after several incidents involving African teenagers prompted Mr Turnbull and Home Affairs Minister Peter Dutton to speak out.
"I had a number of discussions with him before the end of the year, and whilst I don't talk about private discussions I have with the PM, I can confirm for you that despite his recent commentary, he didn't raise these matters with me," Mr Andrews told reporters.
"I might be dobbing myself in for a phone call later today, he might feel the need to now raise these matters with me, having felt the need to rubbish Victoria Police, rubbish Melbourne, rubbish Victoria, that's what he's been
doing."
Mr Andrews backed police Chief Commissioner Graham Ashton's announcement of a joint task force with the African community to tackle the issue.
"We've seen some very nasty incidents in recent times," Mr Andrews said, citing a spate of riots, home invasions, armed robberies, assaults and attacks on police.
"But as someone who proudly lives in Melbourne's suburbs I am completely confident that Graham Ashton and Victoria Police ... are turning this around."
Earlier this month, Mr Dutton took to Sydney radio to say people were too scared to go out to dinner at night in Melbourne.
But Mr Andrews said he took his family out for dinner "a number of times" during his break.
"Mr Dutton's comments were designed to get a rise out of people," he said.
On Wednesday Mr Ashton declared the state one of the world's safest places amid fiery debate over the so-called African youth gang crisis.
The community task force announced is aimed at preventing youth violence and easing racial tensions in Victoria.
South Sudanese leader and solicitor Kot Monoah said members of the community had been unfairly threatened and racially vilified.
"We have a number of people obviously impacted and racially profiled in shopping centres, parks, and this is not a good thing," he said.
The new task force will support police by providing information on emerging issues and hot spots, improving communication on crime prevention and reporting racial vilification.
