Politicians debating the Evening Times' Opt For Life campaign petition said ministers should not wait for an evaluation of a similar Welsh system, due to come into force next year, before making a decision.
The Public Petitions Committee will now a make a bid for a full debate in the Scottish Parliament to move the issue forward.
Welsh Health Minister Mark Drakeford was giving evidence through a video link at a fresh hearing in support of the Evening Times' award-winning campaign.
We are calling for Scotland to change to a system of presumed consent for organ donation. Those who do not wish to have their organs donated would have to opt out of the scheme.
Mr Drakeford said two extra donations a month would cover the running costs of the new system because of the significant costs of kidney dialysis.
The change, which will come into force in Wales on December 1, 2015, is expected to lead to an extra 15 donors a year or 45 potentially life-saving operations.
Angus Macdonald, MSP for Falkirk East, said: "We may not have an evaluation of the system until 2016 or 2017.
"Given that with two donations a month you are covering the running costs of the system, it may be time to encourage the Scottish Government to move faster."
The Welsh minister said the switch would create a "revolution" in the regime of consent and said the process of moving towards legislation, with increased public awareness, had already led to an increase in donor rates.
He explained in detail how the new system would work and took questions from the panel, including Glasgow Labour MSP Anne McTaggart, who queried the cost of implementing the system.
Mr Drakeford said: "It is our belief that the (£7.5million) investment is worthwhile because the system will pay for itself and it will lead to such an improvement in the quality of life of those involved.
"With two extra donations each month, the system will pay for itself. We have more than 200 people on the organ donation waiting list.
"We took extensive evidence of experience elsewhere in Europe and it was clear to us there was a strong association between an opt-out system and levels of organ donation.
"However, I have been out to dialysis units and it is a very powerful testimony when you are sitting next to someone who has been waiting three years for a transplant and they say to you, 'Every day, you have one day less that this miracle can be performed'."
Under the Welsh "soft" opt-out system, the public will have three choices: to opt in, to opt out or do nothing, which will be classed as "deemed consent".
Family members will still have a say but Mr Drakeford stressed they must be representing the wishes of the relative and not their own views.
There will also be an option to appoint a representative to make wishes known in the event of death.
However, the minister said it was impossible to legislate for "every contingency" and that "just because something is law does not mean it is inevitable."
If the clinical team had any doubts, the donation would not go ahead to ensure the public could have confidence in the system.
He said "opting out would be as easy as opting in" and could be done a variety of ways, including at GP surgeries and online.
Tory MSP Jackson Carlaw said the Welsh Assembly had resolved concerns that the committee had about an opt-out system.
Moves to progress the Scottish debate have been welcomed by charities supportive of opt-out, including Kidney Research UK.
Peter Storey, of Kidney Research UK, said: "Waiting lists for transplants of all types continue to increase in almost every country.
"With the prevalence of patients presenting with kidney failure increasing steadily by 4% each year, they will continue to do so.
"We are delighted to hear the Public Petitions Committee has urged the Scottish Government to move forward with a presumed consent debate.
"This development potentially offers hope to those who are waiting for a kidney in Scotland, and we are hopeful the Government will carefully consider the benefits of an opt-out system."
David Stewart MSP, convenor of the Public Petitions Committee said: "Once more I thank the Evening Times for raising the profile of organ donation. The level of this petition merits a specific debate in parliament."
Ms McTaggart has promised to raise a Members' Bill in support of opt-out if the Government does not act.
Evening Times editor Tony Carlin and health reporter Caroline Wilson previously gave evidence to the MSPs at Holyrood and answered the questions on the merits and benefits of an opt-out system.
MSPs asked a series of questions, including: why the paper launched the campaign, the levels of support and why the current donor registration system was not sufficient? Read story here