It's claimed the move will deplete services in some of the city's most deprived areas.
Organs 'Opt-Out' Bill Introduced
A Bill to amend the current "opt-in" system of organ donation has been formally introduced at Holyrood.
If passed, Labour MSP Anne McTaggart's Bill would mean people would have to opt out or their name would be added to the NHS Organ Donation Register.
Ms McTaggart marked the formal introduction of the Transplantation (Authorisation of Removal of Organs etc.) (Scotland) Bill with an event at the Scottish Parliament attended by transplant recipients and their families.
Her proposals already have cross-party support and are backed by organisations including the British Medical Association (BMA).
The Bill will now begin the formal three-stage legislative process at the Parliament.
Ms McTaggart said: "I'm delighted with the success of today's event and that my Bill has been formally introduced at the Scottish Parliament.
"There's still a long way to go in the legislative process but I'm confident that the overwhelming evidence in favour of my proposals will ensure the success of my Bill.
"It was great to see so many people with a strong personal desire to see the implementation of a 'soft opt-out' system in Scotland present at the event.
"Individuals who have had successful transplants, as well as those who are still on the waiting list, and their families were able to meet and discuss the Bill with medical professionals and charities.
"I was also delighted that Lorraine Kelly again reiterated her support and highlighted the importance of starting the conversation about organ donation with your family, which is so important.
"I look forward to working with my colleagues at the Scottish Parliament and with stakeholders as they look closely at the proposals over the next few months."
The BMA in Scotland welcomed the introduction of the Bill.
It said that while progress is being made to improve organ donation rates in Scotland, there are still about 550 people waiting for an organ.
Some of these people will die while they are waiting while others will have died without even reaching the waiting list.
Studies show that up to 90% of Scotland's population supports organ donation yet less than half have signed up to the NHS register.
Dr Sue Robertson, a member of the BMA's Scottish Council and a renal physician, said: "The BMA has long been a supporter of a move to an opt-out system of organ donation, not only because we believe that it would have a positive effect on donation rates, but also because it gives added protection to those who do not wish to donate and makes it more likely that those who are willing to donate will be able to do so.
"The whole transplant community works tremendously hard to increase the levels of organ donation with significant support from the Scottish Government, but there are still people in Scotland waiting for an organ transplant.
"We believe that more can be done and more lives can be saved, and this Bill represents a positive step towards that goal."
Jim McCafferty, 71, who was involved in football in Scotland and Ireland from the 1980s.
The 36-year-old Czech national was arrested on Saturday.
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