About 470 people in Wales are waiting for an organ transplant
A system of "presumed consent" for organ donations may be sought by the Welsh Assembly Government.
Health Minister Edwina Hart has announced that it remains under "active consideration".
She was responding to the assembly health committee's recommendation that ministers should not seek powers to bring in such a system.
Committee chair Jonathan Morgan said he was "disappointed" that Mrs Hart had rejected the committee's conclusions.
In a written response to the committee's inquiry into the issue, Ms Hart said the assembly government believed the findings did not "reflect adequately the evidence it [the committee] received on the strength of opinion" on the matter.
Ms Hart said that once there was "clear understanding of public opinion" the assembly government would consider beginning the process of changing the law".
She added that ministers were "very keen to see improvements in the services and infrastructure" supporting organ transplants.
Mr Morgan, the Conservative health spokesman, said he was dismayed by the minister's response to the committee's conclusions "which were formed after widespread consultation and consideration of all available evidence".
"It would be far better to properly promote, fund and support campaigns to persuade people to become organ donors rather than impose presumed consent in the way the minister appears to favour," Mr Morgan said.
He accused Ms Hart of ignoring "the many religious and moral pitfalls, as well as hypothetical reasons why presumed consent could prove difficult to introduce."
Presumed consent was rejected by a majority of the nine-member health committee in July.
However, nearly half of people surveyed by it said they would like their organs taken automatically after their death to save a life.
The committee said it wanted public sector bodies to do more to encourage people to sign up as organ and bone marrow donors.
Three of its members - two Plaid Cymru and one Liberal Democrat - produced a minority report backing presumed consent.
The committee as a whole voted by six votes to three against 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.
At the time, the British Medical Association (BMA) said it was "extremely disappointed".
The committee's report said: "We do not rule out introducing presumed consent in Wales at some point in the future.
"However, we do not believe that it is currently the most urgent priority and believe that it could be a distraction from other more productive actions."
The Lib Dem AM involved in the minority report, party health spokeswoman Jenny Randerson, praised Mrs Hart's stance as "one of the boldest and bravest decisions" the assembly government had made.
She said: "This vindicates the position of those of us on the committee who felt that the majority report was not in line with the evidence we had heard.
"I'm also pleased that Edwina has strongly suggested that she favours a 'soft' system whereby the views and feelings of the family are always taken into account."
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.
About 470 people in Wales are waiting for an organ transplant.
Transplant charities want Wales to lead the way in adopting a system where organs would be taken from people following their death unless they had opted out beforehand.
A total of 48% of those who responded as part of the Welsh assembly's consultation said they would like their organs to be removed automatically to help save or improve someone else's life.
Another 24% said they would rather put their name on a register, or carry a donor card.
Another 12% said they would prefer their loved ones to decide and only 11% would not want their organs removed at all.