With four weeks to go before a crucial ballot on opening the Swiss labour market to new European Union members, support appears to have fallen.
A poll published on Sunday found just 42 per cent would vote "yes" in September's vote on the issue. This is down from the 49 per cent revealed in another survey almost ten days ago.
Voters are due to cast their ballots on September 25 on whether to extend the free movement of people to mostly eastern European workers.
An accord has given the EU's 15 original members access to the Swiss labour market since 2002.
The survey, published in Le Matin dimanche newspaper and carried out by the Geneva-based Erasm institute, found that only 42 per cent of those asked would vote yes, with 39 per cent against and 19 per cent still undecided.
A different poll published on August 19 found 49 per cent for, 36 per cent against and 15 per cent undecided.
The earlier survey was carried out by the Bern-based GfS Institute for the Swiss Broadcasting Corporation – swissinfo's parent company.
Commenting on the results of the Erasm survey in Le Matin dimanche, Foreign Minister Micheline Calmy-Rey said that previous polls on EU-related votes had also been close and that these latest results were not unexpected.
"We know that the Swiss have fears and that it's also easy for opponents [of the vote] to play on these fears," she said.
Calmy-Rey said that the Erasm survey revealed that the public was still not yet informed enough about the free movement of people and that she would take steps to rectify this.
She also pointed out that the ballot was on opening up the labour market and not about joining the EU.
Scepticism and support
The Erasm poll found that it was mostly young people between the ages of 18 and 34 who remained sceptical about the issue. Only 35 per cent would vote in favour with 43 per cent likely to vote "no".
Overall, support for extending the accord was most prominent in the French-speaking part of the country (47 per cent), among city dwellers (46 per cent) and among those with a university education (60 per cent).
Voters were also found to be divided along party lines. Over 50 per cent support was recorded among the centre-right parties, the Radicals and the Christian Democrats. Among centre-left Social Democrat voters, this rose to 72 per cent.
Only 15 per cent of voters from the rightwing Swiss People's Party said they were in favour, with 75 per cent rejecting the vote.
swissinfo with agencies
The latest poll on the free movement of people, carried out by the Geneva-based Erasm Institute, was published in the Le Matin dimanche newspaper.
1,019 Swiss voters were surveyed by telephone between August 25 and 26.
The margin of error is estimated at plus/minus 3.1%.
In the poll, 42% said they were in favour, 39% against and 19% undecided.
Voters are due to decide whether to extend access to the Swiss labour market to the ten new EU members on September 25.
The accord on the free movement of people is part of the first set of bilateral accords with the EU. This was concluded with the EU's 15 original members in 2002.
Around 18,000 people from the new EU countries, which are mostly eastern European, already live in Switzerland.