According to the Tamedia poll of 15,000 eligible voters, a full 63 percent of those questioned said they would vote yes or were considering voting yes in an upcoming popular vote on the ban, the Tages Anzeiger daily reported.
The Swiss are set to vote on whether they want to ban face coverings in public on March 7, when they will also vote on a range of other issues as part of the country's famous direct democratic system.
The text does not mention Muslim veils explicitly, stating only that “no one shall cover their face in public, nor in areas accessible to the public or in areas where services are ordinarily accessible to all.”
But the proposed ban, which has been opposed by the Swiss government, is widely seen as targeting burqas and other face-covering Muslim veils.
The initiative also makes several exceptions, including in “places of worship”, and, vitally in these pandemic times, for “health reasons”.
The Egerkingen committee which presented the initiative is heavily backed by the populist right-wing Swiss People's Party, but some left-leaning politicians have also joined the campaign in the name of protecting women's rights.
Swiss Justice Minister Karin Keller-Sutter announced this week that the government opposed the nationwide ban, stressing that women wearing full body-covering veils were rarely seen in Switzerland.
She stressed that most women seen in the country wearing such veils are tourists.
The justice minister also insisted the issue should be left up to Switzerland's 26 cantons.
Two cantons, Ticino and St.Gallen, have already introduced such bans, while three other cantons, Zurich, Solothurn and Glarus, have rejected doing so in recent years.
The government and parliament are backing a counter proposal, which would require people to reveal their faces to the authorities for identification purposes, for instance at borders or on public transport.
Fines of up to 10,000 Swiss francs ($11,300, 9,300 euros) could be given to anyone who refused, according to the counter proposal, which will enter into force if the Egerkingen initiative is rejected.