The cartoon, published in response to the continuing assaults on Indians in Australia, particularly the murder of 21-year-old student Nitin Garg in Melbourne last weekend, has been described as "wrong" and "terrible" by the Victoria Police Association and Police Minister Bob Cameron.
The picture allegedly showed a person in a Ku Klux Klan hood wearing a Victoria Police badge, with a caption that "We Are Yet To Ascertain The Nature Of The Crime". The Klan is an infamous white supremacist hate group that had much influence in America during late 19th and early 20th century.
Gillard said she had not seen the cartoon, but believed it would be "deeply offensive".
"Any suggestion of the kind is deeply offensive and I would condemn the making of such comment," she said adding that police were doing an outstanding job in cracking down on crime and increasing Indian students' safety.
"The Victorian Police have stepped up and increased policing in difficult hotspots in Victoria where they have seen a number of violent incidences. They have worked in close collaboration with representatives of the Indian community as they have gone about with this step up in policing," she said.
Police Association Secretary Greg Davies said it was highly offensive to suggest that the police are not properly investigating the murder.
"To say that our detectives are going slow on this, or for some reason trying to protect somebody, is incredibly offensive and wrong," he said adding, "It's based on nothing but obviously a slow news day in Delhi.
"The identity of the offender from the homicide in Footscray isn't even known at this stage, so we don't even know what nationality the offender is. To say it's a race-based crime is not only premature, but stupid," he said.
"It will undoubtedly inflame some people in India and it will undoubtedly inflame some people here in Australia but our people will keep their eye on the ball and they'll get the job done," Davies told a media outlet here.
He said the association would contact its counterpart in India in an attempt to ease tensions.
"I don't know whether they will go in to bat for us. Obviously the media in India are a pretty powerful body but certainly we're going to try and impress upon them the importance of people keeping a level head," he said.
"This sort of thing is just ridiculous, unhelpful, counterproductive and just plain stupid."
Police Minister Bob Cameron termed the cartoon as "outrageous" and terrible."
"Victoria Police is a very tolerant organisation and Victoria is a very tolerant state and to suggest that Victoria Police is racist is just plain wrong and it's offensive to the good police we have here in Victoria," he said.
"To accuse the police of having a closed mind when in fact what police have said is 'we have an open mind to all possibilities' just demonstrates that this is just totally off the table when it comes to common sense," Cameron said adding the cartoon was counterproductive.
"Accusing each other of racism, it just detracts from the plain reality and that is that there's a crime and it has to be dealt with."
Enraged people took to talkback radio this morning to defend the police and their nation.
One of the callers, an African migrant, said he was angered by the cartoon.
"As far as racism is concerned, Australia is one of the least racist countries on the planet," he said.
However, a police officer, Robert, said negative media would not affect the investigation.
"If anyone seriously thinks that Victoria Police homicide squad is not going to thoroughly investigate any homicide based on a cartoon over in India, I think people need to have a bit of a think about what they're getting upset about -- it's just a cartoon," he said.
"It won't stop the homicide squad one iota in doing what they have to do and if anyone thinks otherwise, they're wrong," he said.
Meanwhile, Victoria Police Deputy Commissioner Kieran Walshe said it was understandable that some police officers would find the cartoon "offensive".
However, Victorian police should "stand by our record," he said.
"We have a strong relationship with the Indian community and we know that the Indian community supports the work that Victoria Police has done," he said.