BERN, Switzerland — Swiss voters rejected an initiative seeking to allow local voting on applications for citizenship, dealing a blow to the Swiss People’s Party, the nation’s largest political grouping.

Some 64% of voters rejected the measure, according to final results provided by state-controlled television channel TSR1. All Swiss cantons except one, Schwyz, opposed it. Some French-speaking areas, such as Geneva and Vaud, had a rejection rate of more than 80%.

“It’s a heavy defeat, we lost very clearly,” a Vaud-based deputy of the Swiss People’s Party, Guy Parmelin, said on TSR1. His party colleague Pierre-Alain Karlen called it a “dark” day for “direct democracy.”

The vote is the first electoral defeat since the party quit the government in December and moved into opposition, ending almost 50 years of political consensus in Switzerland. That decision was triggered by the ouster of its most prominent member, the Swiss Justice Minister Christoph Blocher.

In October the party gained a record number of seats at the last parliamentary elections. Its subsequent departure from government brought to an end the formula under which the country’s four largest parties have shared out the seven Cabinet seats among themselves since 1959, ensuring political and economic stability.

The move into opposition may have angered the Swiss People Party’s own voters, the deputy President of the Social Democratic Party, Christophe Darbellay, said on Swiss national radio RSR1 after the vote.

With the initiative, the SVP, as the party is known in German, was seeking to overturn a ban on letting Swiss citizens decide on naturalization bids by foreigners, with no right to appeal. Until 2003, Swiss towns could use popular votes or citizenship committees — sometimes elected or sometimes named by the town council — to grant or deny naturalization applications. Fewer than 5% opted for popular votes.