Labour AM Mick Antoniw called for a new law that could see businesses and insurers foot NHS medical bills for asbestos victims.
The Pontypridd AM, who is a former solicitor representing patients with asbestos-related diseases, introduced the bill in the chamber on 5 December 2012.
"The bill will enable the Welsh government to recover the cost of the medical treatment in cases where legal liability for the disease has been established.
"It is intended that the funds recovered will be used to provide additional assistance to asbestos victims and their families," he told the chamber.
All forms of asbestos were finally banned from being used in the UK in 1999, after it became widely recognised as a serious health threat.
Liberal Democrat AM Kirsty Williams congratulated Mr Antoniw for bringing the bill before the assembly as she looked forward to discussing it in the health and social services committee.
Elin Jones AM for Ceredigion questioned the proposal to return money to the Welsh government and the health minister as she argued the case for the money to be returned to the health boards.
Monmouth AM Nick Ramsay raised concerns that insurance premiums could possibly rise if the companies started paying out more for the claims and that the legislation could also "open the flood gates for other work claims".