Austria's Medical Association has long been insisting that ashtrays should disappear from café tables, pointing to studies which show young people would smoke up to 50% less if smoking was fully banned in cafés and restaurants.
The Vienna Nicotine Institute is also concerned about the health affects of smoke on waiters and hopes current discussions will lead to improved conditions for hospitality workers.
A spokesman for Vienna's hospitality industry, Wilhelm Turecek, doesn't see a problem however. He says a smoking ban has been in place since 2008 - albeit with exceptions - and these were discussed in parliament this January.
Vienna's Health Councillor, Sonja Wehsely (SPÖ), has thrown her support behind Stöger's proposed ban.
"Austria must take the next step," she says. "A smoking ban in restaurants is already normal in Europe."
Doctors at the Austrian Medical Association are calling for 'national solidarity' on the issue.
Current partial smoking bans have failed to lower smoker numbers in Austria, which remain the same as in 2005.
Austrian law prohibits smoking in all enclosed public spaces with certain exceptions for eating and drinking establishments. Smoking in the workplace can be permitted if no employee objects.
However, the smoking ban has been controversial, as the rules are widely ignored by bar and café owners and not actively enforced by the authorities.
One active smoker dies every hour from a smoking related disease in Austria. Three passive smokers die each day.
"Action is needed," said Medical Association head Thomas Szekeres. "Smoking must be prohibited in restaurants and cigarette prices must be raised."