A woman wears a burqa as she walks on a street in Saint-Denis, near Paris. PHOTO: REUTERS
The proposal by lawmaker Walter Wobmann of the populist right-wing Swiss Peoples Party (SVP) won 88 votes, with 87 against.
Wobmann's bill was nearly identical to a measure approved in a 2013 referendum in the Italian-speaking canton of Ticino banning the full-face veil.
The Ticino ban came into force on July 1, and calls for fines ranging between 100 Swiss francs ($100, 92 euros) to 10,000 Swiss francs.
ATS quoted Wobmann as saying that the goal of the national burqa ban was to "maintain public order and respect for the dignity of women".
Just under 30 percent of French Muslims reject secular laws
Tuesday's vote may prove to be a largely symbolic move in the protracted process towards an outright ban on the full-face veil.
Lawmakers will almost certainly defer action on the issue until the country weighs in through a referendum, ATS said.
An initiative has been launched to collect the 100,000 signatures needed to hold a public vote on a burqa ban.
Polls say Swiss voters overwhelmingly support a ban, but a vote could still be two years away.
Even if the ban is endorsed through a referendum, Switzerland's government would still need to draw up a law proposal, which would then be subject to a final parliamentary approval.
Swiss court fines Muslim man for blocking daughters' swimming lessons
Tuesday's vote came as countries across Europe confront tough debates over the role of individual religious liberties, amid rising anti-Islam sentiment that has partly been fuelled by immigration.
France was this summer embroiled in a row over bans on the burkini, a full-body swimsuit, in resorts around the Riviera.
A poll published earlier this month showed Britons are strongly in favour of a burqa ban.
Switzerland's population of 8 million includes an estimated 350,000 Muslims.
The wealthy Alpine nation has seen a number of high-profile disputes involving its Muslim minority, including fines slapped on parents who refused to allow their daughters to take part in swimming lessons, and a case where male students refused to shake the hands of their female teachers.
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