He urged the SPÖ's coalition partner the conservative People's Party (ÖVP) to cease their resistance to the idea of a total ban.
Stöger emphasised that he wanted to achieve smoke-free zones in restaurants and bars within this legislative period. He expects health experts within the ÖVP to support him, saying if there was a corresponding response he would immediately start to implement it.
"It's not expecting too much of Austrians not to smoke in public areas", he said, and pointed to the fact that smoking bans had been a success in other countries.
He said the move would be supported by the majority of the population and would be positive for all, not only for customers but also for landlords and their employees.
Currently smoking in Austria is prohibited in all enclosed public spaces with certain exceptions for eating and drinking establishments. Smoking in the workplace can be permitted if no employee working in the enclosed space objects.
The smoking ban has been a subject of controversy, as the rules are widely ignored by bar owners and not actively enforced by the authorities.
Increasing numbers of Austrians are finding e-Cigarettes - also known as vaping - to be a viable alternative, allowing them to control their nicotine cravings, yet still smoke without restriction in bars and restaurants.
Stöger also expressed his puzzlement with the ÖVP's resistance against other important topics, such as equal rights for homosexuals.