Imported products that contain the cancer-causing agent are also in their sights.
Law firm Maurice Blackburn says it fears there will be a new wave of asbestos victims, if material containing the lethal substance continues to be dumped in landfill.
Just last month, three high-profile cases were discovered in New South Wales, Queensland and Tasmania, with all involving primary schools or daycare centres.
Director of the Asbestos Diseases Research Institute, Professor Nico van Zandwijk, says disposal is a major problem, and perpetrators must be dealt with seriously.
"I think those people who do that, they lack the responsibility for future generations because they dump something that is carcinogenic - which is causing cancer and they don't mind, as long as they got rid of it, and I think it is perfectly appropriate to give those people a very, very high fine because it is criminal action in fact."
Professor Zandwijk says the consequences of asbestos exposure can be devastating, taking 20 to 50 years to develop deadly diseases.
There is no cure for mesothelioma, and the average survival time after diagnosis is just 10 to 12 months.
Inhaling asbestos fibres can also cause lung cancer, asbestosis and benign pleural disease.
Asbestos-containing materials are still found in a third of homes built or renovated before 1987, whether they are cladded with brick, weatherboard, fibro or other material.
Professor Zandijk says there are far too many cases emerging each year because asbestos is being improperly handled.
"Every day you see newspaper articles about demolition of buildings where they later found out there was asbestos present and people didn't take the necessary precautions. It's around and we have to be extremely vigilant to make sure that we know where it is and as soon as we know where it is, then we are able to take the necessary measures to remove it and displace it in the proper way."
While appropriate removal is being labelled a priority, so too are calls for a crackdown on imported building materials that could contain asbestos.
The issue is part of a current senate inquiry.
Head of the Asbestos Department for Maurice Blackburn, Theodora Ahilas, says asbestos being brought in from overseas is a firmly on the political radar.
"We want to be sure the senate inquiry takes a firm approach in addressing the importation of products which may have asbestos in them or do have asbestos in them because it's a mistake to assume that products that are imported don't have asbestos in them. We need to be very vigilant and we need to make sure that the senate inquiry draws good terms of reference as a result of it."
Ms Ahilas says controls should be tightened, while at the same time ensuring asbestos handling more generally is improved.
"Or continue to see that it doesn't become lax in the industry. I think it's very important that we see tighter controls in the importation of product - we've seen an issue this year in relation to imported building products and I think it's very important that in the construction of domestic dwellings that people are vigilant and there's tight controls on that as well because with mesothelioma, you only need a very small exposure to asbestos to develop the disease unfortunately."
With National Asbestos Awareness Month now underway, home renovators are being particularly targeted - with calls for people not to play 'renovation roulette'.
Professor Zandwijk says people must engage experts to safely identify, plan for and manage this potentially fatal material.
Asbestos can be included in roofs, floors, walls, around hot water pipes, fences and even dog kennels.
Managing Director of Science Technology Consultancy CETEC, Dr Vyt Garnys says people shouldn't be fooled - even small jobs can carry an asbestos risk.
"Because even if you create a minor risk, that minor risk can spread to the air in your house, the dust that is not able to be cleaned up for one reason or another and hence the kids can come and play in that dust, or your family and unfortunately, the long term consequences are the ones we need to worry about."
National Asbestos Awareness Ambassador Cherie Barber understands the dangers of asbestos personally.
She says her grandfather died following exposure.
"He was a floor sander, so he was always around fibro-asbestos houses floor sanding but he was also a wharfie in the early days as well, so my grandfather used to come home covered in asbestos dust.My grandmother used to wash his clothes and unfortunately we lost him about 10 years ago to asbestosis so it is a matter that's very important to me."
Anyone thinking about DIY activities is being urged to visit asbestosawareness.com.au
