Two in three Swiss are in favour of increasing the price of cigarettes, according to a survey published on Sunday.
The poll also found that 86 per cent of the nearly 500 people questioned would like to see compulsory non-smoking areas in restaurants.
The survey - published on Sunday in two Swiss newspapers - comes one week after the director of the Federal Health Office, Thomas Zeltner, unveiled new proposals to fight tobacco addiction.
He mooted the idea of increasing the price of a packet of cigarettes in Switzerland to SFr7.50 ($5.90).
The average cost of a packet is currently SFr5.20, but a tax increase of SFr0.50 is due to come into force in the next few weeks.
Zeltner also called for more restrictions on tobacco advertising as well as a ban on tobacco sponsors at sports events.
Of his proposals, only the sponsorship ban failed to win the support of the majority of those polled in the new survey.
The poll, carried out last week, is based on interviews conducted with both smokers and non-smokers.
Just under 40 per cent of smokers, who made up a quarter of those polled, actually favoured an increase in the price of cigarettes.
The remaining 60 per cent rejected the idea.
Two-thirds of all respondents said they would like to see an end to tobacco advertising in newspapers, on cinema screens and on billboards.
Ban for minors
Just over 70 per cent came out in favour of banning the sale of tobacco to minors.
Around 40,000 under-18s are estimated to smoke every day in Switzerland.
Zeltner's proposals include the introduction of a special card for vending machines to make it more difficult for teenagers to purchase cigarettes.
If that proves impossible, he said a ban on the machines should be considered.
Survey respondents were divided over proposals to ban cigarette manufacturers from sponsoring sports and cultural events.
Just under 50 per cent were in favour of continuing to allow the practice, while 45 per cent said they would support a ban on such sponsorship deals.
Last week Zeltner ruled out a complete ban on smoking in restaurants and pubs, saying that this would be difficult to enforce across Switzerland's 26 cantons.
His proposals and the latest poll come just weeks after Switzerland signed an international accord aimed at tobacco prevention.
swissinfo, Elizabeth Meen
One-third of the 500 respondents were smokers.
38% of smokers supported a price increase.
Two-thirds of those surveyed support a rise in the price of cigarettes.
86% favoured designated smoking areas in restaurants and bars.
Two-thirds would like restrictions on advertising in newspapers, on TV and at the cinema.