The bill, which would overturn a ban due to come into force on May 1st, was branded a "huge step backwards for public health" by the opposition.
The far-right Freedom Party (FPÖ) insisted on the ban being dropped as a condition of entering government with the centre-right People's Party (ÖVP) of Chancellor Sebastian Kurz after elections last year.
A petition to keep the planned ban launched by Austria's medical association has now been signed by 420,000 people -- almost five percent of Austria's population.
The opposition Social Democrat Party (SPÖ) has asked health minister Beate Hartinger-Klein to explain how the bill is compatible with Austria's commitments to the World Health Organization.
Several prominent figures within Kurz's own party, including former leader Reinhold Mitterlehner, have expressed their opposition to the ban being repealed. The ÖVP supported the ban under the last government.
But Kurz, despite being a non-smoker and having supported the law under the previous government, says he is bound by his coalition agreement with the FPÖ.
FPÖ leader Heinz-Christian Strache has defended his opposition to the ban, saying it infringes on "freedom of choice" and saying the new plan would protect "smokers, non-smokers and restaurant owners", whose businesses he says would be hit by a ban.
Under current law smokers in bars and restaurants have to be seated in a separate area -- although this is not always rigidly implemented.
But no separate area is necessary in establishments smaller than 50 square metres (540 square feet) if the owner is happy to allow smoking on thepremises.
Some 13,000 people die of tobacco-related causes in Austria each year. The country has the third-highest proportion of smokers in the EU (30 percent of those over 15), according to Eurostat.