The anti-immigration Swiss People's Party (SVP) has won the biggest share of the vote in a national parliamentary election, keeping pressure on Bern to introduce quotas on people moving from the European Union.

Success for the SVP, coupled with gains made by the pro-business Liberal Party (FDP), led political commentators to talk of a "Rechtsrutsch" - a "slide to the right" - in Swiss politics.

Immigration was the central topic for voters amid a rush of asylum seekers from the Middle East and North Africa to Europe.

"The vote was clear," SVP leader Toni Brunner said. "The people are worried about mass migration to Europe."

Sunday's result cemented the SVP's position as the dominant force in Swiss politics.

It won 29.4 per cent of the vote, up from 26.6 per cent in the 2011 vote and far exceeding expectations. It was the best performance by a party in at least a century.

This translated to an extra 11 seats in Switzerland's lower house of parliament to bring its tally to 65, the highest for any party since the chamber's membership rose to 200 in 1963.

The election gains for the SVP, which was already Switzerland's biggest single party, come 20 months after the Swiss in a referendum backed limits on foreigners living in the Alpine nation. The SVP had strongly supported the restrictions.

Lawmakers have until 2017 to reconcile this referendum result with an EU pact that guarantees the free movement of workers, otherwise the Swiss government must write quotas into law regardless of any compromise with the EU.

The Swiss system of direct democracy means citizens decide most major issues in referenda regardless of parliament's make-up.

But the latest right-wing gains should keep pressure on Bern to take a hard line with Brussels as it seeks to implement the immigration referendum.

The left-leaning Social Democrats (SP) finished in second place. Their share of the vote rose 0.1 percentage points to 18.9 per cent but they were set to lose three seats.

The FDP, Switzerland's third largest party, saw its support edge up 1.3 points and was seen gaining three extra seats, tilting parliament further to the right.

The SVP and FDP benefited from a drop in support for the centrist BDP and the two green parties.

During the election campaign, the SVP rallied against Swiss reforms to deal with asylum seekers, even though in Europe's current migrant crisis Switzerland is handling far fewer migrants than some other nations such as Germany.