Some 92 percent of the 1,030 people who answered the survey in Mumbai, New Delhi, Chennai and Kolkata, strongly favoured curbs on lighting up at work or in hotels, bars, restaurants, cinemas, schools and hospitals, it said.
Eighty-four percent also agreed that breathing second-hand smoke was a serious health hazard, mirroring the findings of similar surveys conducted in other countries that have now gone smoke-free.
India has some 120 million smokers -- about one-fifth of the population. A study published in the New England Journal of Medicine in February this year said one in every 10 deaths in India from 2010 would be smoking-related.
Laws already exist to prevent smoking in public places and ban mass media advertising of tobacco products, except at sales points. But the government has struggled to enforce them and fines for offenders are small.
Tougher regulations come into force on October 2.
Medical experts behind the new poll, conducted by the Healis Sekhsaria Institute for Public Health in Mumbai, said the rules would be easy to enforce since they better defined what was not allowed.
"The current notification could not be implemented very well because of loopholes," Healis director Dr Prakash C. Gupta told a news conference in Mumbai, which next year hosts the 14th World Conference on Tobacco or Health.
"It was weak because it allowed smoking areas, without exactly specifying the meaning of a smoking area. This time the notification is very, very clear and there is no ambiguity."
The head of pharmaceutical firm Johnson and Johnson India, Narender Ambwani, a former smoker whose company went smoke-free in 1995, said popular support was vital to making the law work.
"If people know they can complain and can object (to smoking)... they can challenge it. Public awareness needs to be built up so that non-smokers have a right to tell smokers not to smoke," he added.
"Once that comes in then the implementation will be far better."