Our petition calling for the change, which has been signed by more than 20,000 people, took centre stage at Holyrood yesterday and was given cross-party support.
Praising our campaign, Jackson Carlaw, Conservative MSP for the West of Scotland, said it was the first time politicians had been asked to vote on the issue in Parliament.
Health Minister Michael Matheson said the Scottish Government was standing firm on a decision to await a review of the Welsh opt-out system - due to come into force next year.
However, his views were not supported by the majority of MSPs, with only one politician, the SNP's Christine Grahame, voicing strong opposition.
MSPs said they would support a free vote on the issue, which could increase the likelihood of legislation being passed, given the strong level of support amongst Scottish politicians.
Mr Matheson said the personal views of Deputy First Minister Nicola Sturgeon and Health Secretary Alex Neil, who have previously voiced support for opt-out, had "not changed".
Glasgow Labour MSP Anne McTaggart reinforced her commitment to introducing a Member's Bill calling for the change because of the "compelling evidence" that it will lead to increase in the number of donors.
She said: "It is my ambition that organ donation will become the default position.
"Through the evidence presented, I have been convinced an opt-out system would be in the best interests of patients.
"The Welsh system will result in 45 more lives being saved every 12 months. Individuals will have exactly the same choice, to donate or not to donate."
There was a wide consensus amongst MSPs that moving to an opt-out system would make it easier for families to make the "agonising" decision on whether to agree to donation because it is more likely that their loved ones wishes will be known.
Bob Doris, SNP MSP for Glasgow, said: "I have looked on in admiration at this petition.
"It is clear there are many aspects (of an opt-out system) that are much more acceptable than the current system. I think it is very important we continue to take this forward.
Glasgow Labour MSP Drew Smith said: "Under the current system we have no guarantee our wishes will be respected. I believe it is a simple change that will save lives."
Jim Hume, Liberal Democrat MSP for South Scotland, said it was time for an "open and robust" debate on the issue and said the priority would be to "reach a point where donation is the norm."
Chic Brodie, SNP MSP for South Scotland, said: "This is a brave petition because it confronts the emotive issues of organ donation."
About 650 people in Scotland are waiting for a donor organ.