The Wales province in the United Kingdom is moving to have opt-out system incorporated in the organ removal process.
Wales, like the rest of the UK, currently has an opt-in organ donation system - people who want to donate their organs after their death must sign up to the Organ Donor Register.
But there is growing support for a "soft" opt-out system - also known as "presumed consent".
Health Minister Edwina Hart has launched a consultation on proposals to introduce the opt-out system in Wales.
Under such a system, which is in use in Belgium and Spain, people who do not want to be considered as organ donors would have to register their decision to opt out.
But relatives would still be consulted about, and have the right to veto, organ donation.
Opt-out systems have been credited with increasing the number of organs which are available for transplant.
There are currently more than 500 patients in Wales waiting for an organ transplant. The majority are waiting for a kidney.
Dr Richard Lewis, Welsh Secretary of the British Medical Association, said: "There is little doubt that such a system would produce a far higher potential donor rate than at present, which is far too low at 22%.
"Experience of other European countries that have already introduced an opt-out scheme have proven this to be the case.
"In previous public opinion surveys, the vast majority of people say they would be willing to donate their organs. Unfortunately, this does not translate into people who actually sign the register.
"This is where the crux of the problem lies. People want to be donors but, for whatever reason, they just do not get round to signing the register.
"Of course, that would not be an issue with an opt-out system, and that is how a change to legislation could make all the difference to anyone left waiting on the organ donor register."
The 12-week consultation, which ends on August 3, will ask whether Wales should change the law on organ donation and follows a major public debate between October and January.
In a letter launching the formal consultation Mrs Hart said: "It is clear that there is significant support for increasing organ donation rates and a wide range of suggestions were put forward on how this might be achieved, including possible changes to the consent system.
"The public debate confirmed that there is an appetite for change to the organ donation consent system with the feedback suggesting a preference for a soft opt-out system.
"The aim of this further consultation exercise is to find out if the Assembly Government should now move forward and propose legislative change."
Mrs Hart has also commissioned officials to advise the Assembly Government about what legislative options are available to Wales if it decides to go down this route.
Roy J Thomas, chairman of the Kidney Wales Foundation, said: "This is an important step forward for those waiting for a transplant and sends a genuine message of hope.
"It is important that members of the public are given the chance to express their views on this issue and engage in the debate, which is why we welcome this latest step by the Health Minister.
"Through the introduction of an opt-out system of organ donation and more donor co-ordinators many more lives can be saved in Wales.
"The brutal reality is that people in Wales waiting for a transplant are dying because of the shortage of donors - statistically, it's one person every 11 days.
"We stand at a crossroads where the urgency for change has never been greater.
"Kidney Wales has looked carefully at the way in which other countries in Europe have benefited from the introduction of an opt-out system.
"In the 23 years since this system of organ donation was adopted in Belgium, for example, many more hundreds of lives have been saved in comparison to Wales.
"A responsible and factual debate on this health issue is needed.
"A change to an opt-out system of organ donation, coupled with the introduction of more donor co-ordinators in Welsh hospitals, would lead to hundreds more lives in Wales being saved by the gift of organ donation."
Belgium introduced its "soft" opt-out system in 1986 and increased the number of transplant co-ordinators at the same time.
Just 2% of the population has opted out of organ donation - by registering at their local town hall - and the national rate of organ donation rose by 55% within five years.
The latest figures show that in Belgium there were 291 deceased organ donors in 2007 compared to only 51 in Wales - Belgium has one of the highest rates of donors per million people in the world.
Andrew RT Davies, the Welsh Conservatives' Shadow Health Minister, added: "We welcome any moves that can lead to an increase in the number of people on the organ donor register.
"With one person dying every 11 days in Wales waiting for a transplant, it's clear more needs to be done to increase the numbers of donors. However the Assembly Government must ensure that any moves to increase the number of organ donors are coupled with moves to add to the number of donor co-ordinators in Welsh hospitals.
"There is no point increasing the number of organs available for transplant if the Welsh health system cannot cope."