LibDem MSP Jim Hume said the majority of the 161 responses to his consultation showed an appetite for the crackdown and said he now had cross-party support from 25 MSPs for his Member's Bill.
The position puts him at odds with Deputy Prime Minister Nick Clegg, the Lib Dem leader at Wesminster, who said enforcing a ban would not work, although the House of Lords has backed a Labour Bill making it a road traffic offence, with fines or points on the licence of the driver for allowing smoking with children present.
But Mr Hume said it should be treated as a health issue, which is why his Bill has received clearance from the Holyrood authorities.
He said: "These are fair and specific proposals whose time has come."
The responses showed backing from every charity or body in the health sector and the only opponents were the tobacco industry.
Mr Hume lodged draft proposals for a Bill in May last year calling for a ban in Scotland on smoking in private vehicles while a child under 16 is present.
Motorists could be fined £60 for breaching the rule.
Consultation responses were split among 88 sent to Mr Hume and 73 completed through an online survey by the British Heart Foundation.
It showed 75% supported the plan, rising to 84% when the survey was included.
Some concern was raised about how police will be able to identify the age of passengers and offenders.
The Tobacco Manufacturers' Association and smokers' lobby group Forest said the plan is a disproportionate response to a relatively rare problem.