Geneva (AFP) - The Swiss voted Sunday for a new parliament, with initial results and projections showing the populist right significantly strengthening its already dominant position amid concerns over migration and asylum rules.

The first results ticking in from Switzerland's 26 cantons showed the country's largest party, the populist right-wing anti-immigration Swiss People's Party (SVP), making gains that were expected to tip the scale in parliament towards a slight centre-right majority.

Observers had predicted that SVP would gain ground from the 26.6 percent of the vote they won in 2011, but initial regional results showed their support swelling more than expected and even possibly passing their all-time high in 2007 of 28.9 percent.

In all, 246 seats are up for grabs -- 200 in the lower chamber and the remainder in the upper chamber.

The expected shift comes as surging numbers of migrants and refugees moving through Europe have heightened the focus on the issue in Switzerland, even though the wealthy Alpine nation is yet to be significantly affected by the crisis.

About a quarter of Switzerland's eight million inhabitants are foreign nationals, and immigration and asylum policies tend to figure among voters' top concerns.

- 'A lot at stake' -

The latest survey from the gfs.bern polling institute showed that nearly 50 percent of voters considered migration the most important issue facing the country.

"I think there is a lot at stake, not only when it comes to the reception of refugees, but also the entire problem of the large numbers on the move," Colette Morel, a 69-year-old retired teacher, told AFP as she cast her ballot in the central canton of Fribourg.

SVP vice president and its most outspoken member, Christoph Blocher, insisted earlier this month that his party was the only one that could solve Switzerland's "asylum problem" and "eliminate the chaos".

Blocher, a multi-billionaire who served in the Swiss government from 2004-2007 before being pushed out over his confrontational style, saw his daughter Magdalena Martullo Blocher win a parliamentary seat Sunday in the eastern canton of Graubunden, the early results showed.

Story continues

The SVP, which has previously sparked outcry with campaign posters such as one showing three white sheep kicking a black sheep off the Swiss flag, has in its national push this year been less provocative, resorting mainly to posters featuring pictures of candidates with the slogan "Stay free".

But some regional divisions of the party have gone much further, with the Vaud youth unit putting out a poster featuring a caricature of a jihadist, wearing an EU armband, preparing to decapitate a bound and gagged blonde woman wearing a Swiss flag tank top, flanked by the caption: "Keep your head on your shoulders".

That poster also plays to the second top concern among the Swiss, according to the latest gfs.bern poll.

Nine percent of those questioned in the survey said they were most concerned about Switzerland's relationship with the European Union, which was badly hit by a narrow Swiss popular vote in February 2014, championed by the SVP, in favour of restricting immigration from the bloc.

The centre-right Liberals, in third place, were also seen gaining ground, according to the first results, helping move the pendulum in parliament towards the right.

The party, which largely sees eye-to-eye with SVP on economic and energy issues, takes a very different stance on a range of subjects, including on the question of immigration.

- Magic formula -

The Socialists, Switzerland's second largest party, were meanwhile seeing mixed results Sunday, snatching an extra seat in Zurich but losing one seat in Valais and another in Vaud, early results showed.

The Christian Democrats, the Greens and other smaller parties were seen taking a hit.

Power-sharing and consensus rule are the norm in Switzerland and elections rarely lead to major shifts in parliament or the makeup of the government, which does not directly reflect the power balance in the house.

Once the new parliament is in place, it will in December elect the government, with the seven posts traditionally shared among the major parties from right to left under a tacit decades-old agreement dubbed "the magic formula", aimed at ensuring political stability.