An opinion poll has said that some 35 percent of Russians support an initiative to introduce a 3,000-ruble ($100) fine for smoking in public places.
The poll by the Public Opinion Foundation found 34 percent said the fine would be too big, whereas 19 percent do not approve of the initiative at all, five percent said the fine was too small and seven percent were undecided.
Most respondents (61 percent) said they are against banning smoking lounges at workplaces, while 22 percent backed the idea.
Russia's lower house of parliament, the State Duma, approved a ban on smoking in public places Jan 25.
It envisages a gradual ban on smoking in public, including government buildings, healthcare and educational facilities, cultural sites, sports stadiums and public transport.
Further amendments to the anti-smoking bill, such as banning smoking lounges at workplaces, were not included in the final version.
The poll also showed that most Russians (51 percent) believe the new anti-smoking law will not affect the number of smokers, 40 percent said it will change the situation.
The poll was conducted Jan 26-27 among 1,500 residents of 43 Russian regions.
The legislation also imposes a blanket ban on tobacco advertising.
Tobacco companies will be barred from holding promotional prize draws and sponsoring public events and competitions.
The bill may also prohibit the display of tobacco products in shops.
The law is due to come into force June 1, 2013, though some of its provisions, including a total ban on smoking in trains and hotels, will come into effect next year.
Russia signed the Framework Convention on Tobacco Control with the World Health Organization in 2008. This obliges Russia to enact tougher restrictions on tobacco by 2015.
According to a survey conducted by the Levada Center in November, only 18 to 31 percent of respondents supported an outright ban on smoking in workplaces, airports, restaurants, bars and hotels, while up to 75 percent believe smoking should be restricted to specially designated areas.
Around 40 percent of Russian adults smoke.