More than 27% of Swiss voters say the climate crisis will be a determining factor in their vote, prompting predictions of a green surge and a fall in support for the nationalist Swiss People’s party (SVP) in parliamentary elections on Sunday.

Most voters have already cast their ballots by post in the nationwide poll, which elects 245 members of Switzerland’s federal assembly – 200 to the lower house, known as national council, and 46 to the upper house, the council of states.

The executive that will govern the country for the next four years, known as the federal council, will not be be decided until 11 December, with its seven cabinet positions divided among the four biggest parties in the two lower houses.

Polls suggest the Greens, forecast to win more than 10% of the vote, against 7% in the 2015 elections, could overtake the centre-right Christian Democrats to take fourth spot and secure their first federal council seat.

The Greens would be far more likely to claim a place in government if they join forces with the smaller Green Liberals party, which is also polling strongly at 7%, although the parties differ on issues including economic policy and may not be able to agree on a single unity candidate for a ministerial job.

However, the vice-president of the Greens, Lisa Mazzone, told Agence-France Presse: “We have every intention of being a force in government, because I believe that is what Switzerland needs.” Polls show the party is benefiting particularly from strong support among first-time voters and people who have previously abstained.

The Swiss People’s party, arguably Europe’s most consistently successful rightwing populist party, is widely expected to remain the largest party, although support for its often virulently anti-immigration platform appears to be slipping. It took a record 29% of the vote in 2015 and is now polling at 27%.

Levels of concern about immigration have fallen significantly, according to polling for the state broadcaster RTS, with only 19% of voters saying it will determine how they vote – behind climate change, healthcare premiums and relations with the EU.

Michael Hermann, of the polling firm Sotomo, told RTS the shift from immigration to climate as the country’s top political issue was one of the most dramatic pivots he had seen in Swiss politics. The “green wave is rolling along”, he said.

The SVP is the only party currently on Switzerland’s federal council to contest the reality of the climate crisis, with both the Socialists and the two centre-right parties pushing markedly environmentally friendly policies.

Last month 100,000 people – a significant turnout for a country of 8.5 million – marched through the Swiss capital, Bern, demanding comprehensive climate action from the next government.