The SVP took 29% of the vote in elections to the lower house of parliament, improving its vote share by more than three percentage points, predicted market research group GFS Bern, which conducted the main polling throughout the election campaign.
Polling stations closed at noon, the vast majority of Swiss voters having posted in their ballots over the past four weeks.
The SVP came well ahead of the left-wing Social Democrats on 17%, while the centre-right party The Centre, and the rightwing party called FDP. The Liberals, were both on course to finish on around 15% - with all three chasing parties largely flatlining.
Meanwhile the Greens could not replicate their dramatic gains at the last election in 2019 and slid back four percentage points to finish fifth on nine%, according to the projection.
"It was too late to send it by post but given that it's important, I told myself I would still come today," voter Melanie Salamin told AFP at a polling station in the capital Bern.
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