The vote against it was 70.7 percent according to official results in a referendum that had a 55.5 percent turnout.
Under Switzerland's direct democracy system, 100,000 signatures are needed to put virtually any issue to a popular vote.
That gives voters a say on a wide range of topics every few months at the national, regional and local levels.
Under the initiative launched by the Social Democratic Party and the Greens, the country would have spent 0.5-1.0 percent of Switzerland's annual GDP -- around 4 to 8 billion Swiss francs ($5-10 billion) -- on fighting climate change.
The idea was to move the country towards its target of carbon neutrality by 2050.
Both the Swiss government and the parliament had urged voters to reject the initiative, arguing it would be too expensive.
They pointed out that the country already spends around two billion francs a year -- from a budget of around 90 billion francs -- on climate protection.
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