Smoking in cars when children are on board is expected to be banned within the next 12 months.
Public health minister Maureen Watt confirmed the SNP administration would support proposals which could see people fined £100 if they are caught lighting up in a vehicle when under-18s are present.
Liberal Democrat MSP Jim Hume has submitted a member's Bill at Holyrood in a bid to change the law.
While Ms Watt said the Government supported the principle of his Smoking Prohibition (Children in Motor Vehicles) (Scotland) Bill, she also said changes would need to be made to the legislation to ensure it is workable.
Ms Watt said: "This Government is absolutely committed to protecting children from the harmful effects of second-hand smoke.
"Last year we announced a target to reduce the proportion of children in Scotland exposed in the home from 12 per cent to 6 per cent by 2020 - potentially saving 50,000 Scottish children from second-hand smoke.
"Mr Hume's Bill chimes with those aims and we have always been clear that we supported the proposals in principle.
"We consulted on the possibility of including this measure in our forthcoming Public Health Bill, but we have now decided to support this members' Bill.
"As with any Bill, as it goes through the scrutiny process there may be amendments and improvements to strengthen the legislation and ensure it is fit for purpose.
"But we believe that the underpinning principles are strong and that is why I am pleased to support it."
Mr Hume's proposals have already been backed by Scottish Labour and a number of health charities.
Mr Hume, the Scottish Liberal Democrat health spokesman, said: "I am over the moon that the Scottish Government is to support my moves to ban smoking in cars while children are present.
"With cross-party support and the support of many third-sector organisations, there is every chance that this could be in place in the next year."
He added that 84 per cent of the 160 responses to his consultation backed the change, saying that "people from across Scotland have expressed their support for the move".
Mr Hume added: "This Bill is about guaranteeing that children in Scotland can have the freedom to go on and lead healthy lives if they choose to.
"I look forward to working with MSPs from all parties as the Bill progresses."
Anti-smoking campaigners welcomed the Scottish Government's backing for the Bill.
ASH Scotland chief executive Sheila Duffy said: "We are delighted that ministers have decided to support this important member's Bill, which has the potential to protect thousands of our children from the dangers of breathing second-hand tobacco smoke.
"It is another public-health initiative that can help Scotland move forward with its ambition to achieve a tobacco-free generation in 20 years' time.
"It is popular with the public and will bring Scotland into line with upcoming legislation in England and Wales.
"We believe it can be effectively enforced and that having the legislation focus on cars with children bypasses concerns over interference in people's private lives.
"Jim Hume must be congratulated for taking the initiative on this proposal and for all the hard work he and his team have done to bring this important measure forward."
Simon Clark, director of the smokers' group Forest, branded the Bill as being "legislation for legislation's sake".
He added: "Smoking in cars carrying children is inconsiderate. The overwhelming majority of smokers know that and don't do it.
"The very small number that do will carry on regardless because the law will be difficult, if not impossible, to enforce.
"Education has to be better than legislation but the Government prefers gesture politics and the big stick."
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