The report said smoking in cars exposed children to cigarette smoke
The Scottish government said there were currently no plans to ban smoking in private cars and public areas used by children.
The comments came in a response to a report by the Royal College of Physicians.
It said smoking in cars was an "important and persistent" factor in exposing children to cigarette smoke.
Campaign group Forest, which opposes smoking bans, said such moves would be unacceptable and unenforceable.
Banning smoking in cars would be "the simplest means" of preventing children from being exposed to dangerous tobacco smoke in vehicles, the Royal College of Physicians report concluded.
Dr Neil Dewhurst, president of the Royal College of Physicians of Edinburgh (RCPE), said: "Passive smoking exposure levels in children have fallen by 40% in Scotland since the introduction of smoke-free legislation, but exposure levels in children of smokers remain high and demand further legislative action.
"We fully endorse today's report which calls for an extension of smoke-free legislation throughout the UK in order to include public areas frequented by children and in cars.
"The evidence is compelling. Passive smoking exposure significantly increases the risk of a range of diseases in children."
Mr Dewhurst said Scotland had led the UK in the introduction of smoke-free legislation and he called on the Scottish government to extend this legislation as a matter of priority.
A Scottish government spokesperson said: "The successful implementation of the smoke-free legislation has undoubtedly reduced exposure to second-hand smoke among children in Scotland, partly as a result of the greater awareness among their parents and those close to them about the risks of second-hand smoke.
"While there are currently no plans to extend the smoke-free laws to private cars, the Scottish government is conscious that private cars are now one of the main places for exposure of children to second-hand smoke.
"In conjunction with our health improvement partners, we are continuing to do all we can to highlight the risks posed by second-hand smoke."