Currently around 470 people in Wales are waiting for an organ transplant
A series of debates are to be held to gather public opinion on "presumed consent" for organ donations in Wales.
Health Minister Edwina Hart wants to gauge public opinion on whether the assembly government should seek a legislative change.
Last week Ms Hart rejected the assembly health committee's recommendation that ministers should not seek powers to bring in such a system.
Events will be held and a discussion document will also be issued.
Unlike the current 'opt-in' system, presumed consent is an 'opt-out' system where it would be presumed organs would be available for transplant unless an individual had formally registered against it.
Ms Hart said: "Around 470 people in Wales are currently waiting for an organ transplant, but with a desperate shortage of donors many face the reality of having to wait years and the possibility they may even die while waiting.
"Although the assembly government is already funding campaigns to increase the number of donors, a shortage of organs still remains so it is my belief that we should examine more closely the issue of introducing a system of presumed consent."
In July, the nine-member health, wellbeing and local government committee rejected the idea of adopting the system of presumed consent for organ donation.
They voted down a proposal to apply for a Legislative Competence Order (LCO), which would give the assembly the power to bring in such a system in Wales, by six votes to three.
Ms Hart said she did not believe the committee's report "adequately reflected the evidence it received in relation to presumed consent".
Ms Hart said she was committed to increasing capacity in transplant services
Nearly half of the people surveyed for the report said they would like their organs taken automatically after their death to save a life.
"However, I recognise that any changes to legislation would require further wide-ranging consultation and testing of public opinion as this is a sensitive and emotive issue," Ms Hart added.
The debates and discussion paper will examine the public's view of a range of systems such as 'hard' and 'soft' presumed consent.
A distinction is often drawn between 'soft' and 'hard' versions of an opt-out system.
In the 'soft' version relatives are allowed to veto the removal of the organs of their relative, and in the 'hard' version, this veto is not present.
The soft version can be found in Belgium and Spain, and the hard version in Austria.
The public will also be asked whether certain organs should be excluded from any new system.
Mrs Hart added: "Regardless of whether we go down the route of introducing a system of presumed consent, we are committed to encouraging more people to become organ donors.
"We are also committed to increasing capacity in transplant services, as shown by our investment in a new renal transplant facility in south Wales."
Prime Minister Gordon Brown has spoken in favour of presumed consent and a UK Government taskforce is due to report on the issue over the next few months.