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.
