GENEVA, Switzerland (AFP) — Swiss voters will decide the fate of a divisive anti-immigration proposal on Sunday to cap the country's population, and another referendum on restricting access to conscientious objection to military service.

Opinion polls suggest that both votes, put forward under Switzerland's direct democracy system, could be tight.

Voting booths will open for just a few hours Sunday morning before closing at noon, most of the votes having been cast in advance by post. The first results are expected by mid-afternoon.

Tensions have been running particularly high over the "No to a Switzerland with 10 million!" initiative, put forward by the hard-right Swiss People's Party (SVP).

That proposal wants measures to stop the wealthy Alpine nation's population — currently 9.1 million — going above 10 million before 2050.

In a country where foreigners make up over a quarter of the population, the proposal, if accepted, would slam the brakes on immigration.

The SVP, Switzerland's largest party, insists drastic measures are needed, blaming "mass immigration" for a whole host of problems, from housing shortages and rising rents to overcrowded trains and traffic jams.

"Switzerland is a small country that cannot be expanded," SVP parliamentarian Yvan Pahud told Agence France-Presse.

We "do not want to welcome all of Europe."

But critics warned that, if passed, the initiative could cause "chaos," possibly crippling swathes of the economy and Switzerland's relations with the European Union, its main trading partner.

"The stakes are very high," Swiss Justice Minister Beat Jans told the Tribune de Geneve newspaper, warning that the vote could provoke the equivalent of a Swiss "Brexit."

The initiative faces broad opposition from the government, parliament and multiple sectors of the economy.

While opinion polls suggested the vote could be tight, the latest surveys indicated opposition to the proposal nudging ahead.

For it to pass, it would need to win not just a majority of votes cast but also majorities in more than half of Switzerland's 26 cantons.

Conscientious objection

The Swiss will also vote Sunday on a bill passed by parliament to make civilian service less attractive and less accessible, at a time when the war in Ukraine and other geopolitical tensions are pushing European countries to bolster army numbers.

It was the political left in the militarily neutral country that called the referendum. They argue the bill is dangerous and could ultimately lead to the alternative to military service being scrapped altogether.

Here too, opinion polls suggest the vote will be close.

Switzerland has compulsory military service for men. They serve in a unique militia system in which army conscripts do at least four months' service before being called up repeatedly over a decade for weeks-long refresher sessions.

People who conscientiously oppose military service have since 1996 been permitted to perform civilian service instead.

Since access to civilian service was simplified in 2009, the numbers choosing that option have steadily climbed — a trend the government warns has become "problematic."