The initiative was launched by a right-wing, Eurosceptic party Switzerland People's Party (SVP), which has two seats in the seven-member government and the largest group of deputies in the parliament.
In Switzerland, the population is growing rapidly and last year 9,1 million people lived in that country, more than a quarter of whom do not have a Swiss passport.
Statisticians predict that the population will reach ten million around 2040, Swiss media write.
The SVP initiative, which consists of several phases, envisages that the moment the number of 9,5 million is reached, the right to asylum and the right to family reunification will be restricted.
The Swiss constitution already states that Switzerland independently manages migration and limits it with annual quotas and quotas. However, that constitutional provision does not apply to the treaty on freedom of movement with the EU.
By reaching the limit of ten million, the Swiss parliament would have to apply drastic measures, including the termination of the contract with the EU from 2002.
In a poll that included 19.400 Swiss between May 19 and 27, 52 percent voted against the SVP proposal, while 45 percent were in favor and the rest were undecided.
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