Initial results Sunday showed Swiss voters rejected a measure to cap the country's population.
The right-wing Swiss People's Party, the country's largest political group, seeks to curb immigration and limit the population to 10 million by 2050.
The country is home to about 9.1 million people.
Vote counting began at noon (10 a.m. GMT). Lukas Golder of the survey institute gfs.bern told Swiss broadcaster SRF soon afterward that the "no" vote was ahead.
For much of the campaign, opinion polls indicated majority support for the proposal. But surveys in recent weeks pointed to a shift in sentiment, suggesting a tighter race.
The outcome was expected to be close, though Swiss referendum results often diverge from polling forecasts.
If approved, the initiative would require the government to restrict asylum and family reunification once the population reaches 9.5 million, a milestone likely to be reached in the 2030s.
If those measures are insufficient, Switzerland must end its free-movement agreement with the European Union. The accord allows reciprocal rights to live and work across borders, though Switzerland is not an EU member.
