The British Medical Association (BMA) is calling for urgent action after it estimated 30 people died waiting for organ transplants in Wales in a year.
From BBC News
It said it believed the assembly government should introduce a "soft" system of presumed consent.
An assembly health committee last year said ministers should not seek powers to bring in such a system, where people would have to opt out of being donors.
Health Minister Edwina Hart is now considering responses to consultation.
BMA Cymru Wales submitted a response to the consultation, saying the current organ donation process needed to be overhauled "sooner rather than later, before more lives are lost".
It estimated that 30 people died while still on the organ donation register in the past year in Wales - with 150 people dying in the last five years.
Dr Richard Lewis, Welsh Secretary of the BMA, said a system of presumed consent would produce a far higher potential donor rate than at present.
"The main difficulty with the current system is that where, as in the majority of cases, relatives do not know what their loved ones wishes are, they frequently, and understandably, opt for the default position, which is not to donate," he said.
"This would be addressed by the introduction of an opt-out system where the default position would change in favour of donation.
"We recognise this is a subject many people hold strong views about and as such, those who do not want to donate their organs will sign up to opt out."
He urged the assembly government to take action and apply for the legislation needed to bring in a new system.
"The time really has come, before more people die waiting in vain, the Welsh Assembly Government needs to stop procrastinating and seek an LCO (Legislative Competence Order) from Westminster to bring in a soft system of presumed consent," he added.
However, the British Organ Donor Society is against the opt-out system, saying they think education is the key.
Chairman Ray Pearson, whose daughter donated organs to seven people after she died in a road traffic accident, said: "The answer to the problem is education. The best form of education is is the education of children. The children then will educate the parents."
Joyce Robins, co-director of the patients' group, Patient Concern, said: "The BMA is using its considerable influence to mould public opinion on the basis of misinformation and distorted facts about the supply of organs".
She added: "They make sweeping statements about presumed consent producing a far higher number of organs".
In September 2008, the health minister rejected the assembly health committee's recommendation that ministers should not seek powers to bring in presumed consent.
She then ordered a series of debates to gather public opinion on possible changes to organ donations in Wales.
A spokesman for the assembly government said officials were now considering the results of the consultation.
"We have held a public debate on the possibility of changing legislation and have consulted on options to increase organ donation," he said.
"Officials are now considering the responses to the consultation and will be advising Mrs Hart on options available to the assembly government."
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