First results showed Swiss voters rejecting a measure to impose a cap on the country's population on Sunday.
The right-wing Swiss People’s Party (SVP), Switzerland’s largest political party, is seeking to curb immigration and limit the population to 10 million by 2050.
The Alpine country is currently home to around 9.1 million people.
Vote counting began at noon (1000 GMT), with pollster Lukas Golder from survey institute gfs.bern telling Swiss broadcaster SRF soon afterwards that the "no" vote was ahead.
For much of the campaign, opinion polls indicated majority support for the proposal.
However, surveys conducted in recent weeks have pointed to a shift in sentiment, suggesting a much tighter race.
The outcome is expected to be close, although referendum results in Switzerland have frequently diverged from polling forecasts.
If the initiative is adopted, the granting of asylum and family reunification would have to be restricted once the population reaches 9.5 million. That is likely to happen in the 2030s.
If those measures prove insufficient, Switzerland would have to end its freedom-of-movement agreement with the European Union, which allows reciprocal rights to live and work across borders, even though Switzerland is not a member of the bloc.
