Brumby condemned any racist attacks and said he had requested another meeting with Singh, who is heading home next week to discuss the attack crisis, the AAP reported.
Singh reportedly criticised Victoria for being in a state of denial over the scale of the problem and falling behind New South Wales, Queensland and South Australia in tackling racist attacks.
Premier Brumby said he would brief Singh on the progress that had been made, including boosting police patrols in high risk areas like railway stations and toughening up police powers to search for weapons.
"I'll be able to inform her of all of these things and again to reassure her that Victoria is a much safer place than other places in Australia and indeed around the world," he said.
Reiterating his stance on a "fair and balanced debate" on the issue, Brumby said the recent cases purporting violence against Indians, including a man who allegedly set himself on fire as part of an insurance fraud and a murder allegedly committed by an Indian couple, had unfairly damaged Australia's reputation.
"There's always a lot of speculation about these things but if you look at the facts of the matter... in relation to assault, in relation to Indian students, they are under-represented in terms of their population share. I think it's important in this discussion and this debate that there's some balance in the reporting and in attitudes that are expressed publicly," he said.
Meanwhile, the Age reported that Brumby mooted a possible Indian taskforce for tackling racist attacks that is said to merely formalise work already being carried out.
Brumby is also meeting cricketer Shane Warne tomorrow to discuss promotion of Australia in the sub-continent, including a possible friendship cricket game.
"Where things are wrong, where an assault has occurred, particularly if it's racially motivated I've condemned it in the strongest possible terms and police have devoted every possible resource to both preventing crime as well as apprehending those who have committed offences," he said.
Brumby also cited Victoria's lowest crime rate and that the Indian population was under-represented in terms of assaults. He stressed that if the state was a dangerous and racist place then overseas students would not be coming here.
Melbourne Lord Mayor Robert Doyle was quoted as saying that everyone needed to "take a deep breath".
"Let's take the colour and the race out of it and just try to get to the root of the problem and fix that, and remember whether they're Indian or Chinese students or Australian nationals these are young people in our streets who are being injured and who feel, very threatened," he said.
