Two out of three Swiss appear to approve closer cooperation on security and asylum with European Union member countries.
A survey also shows that a majority of potential voters do not object to differences of opinion within the cabinet on the Schengen/Dublin accords.
Sixty-eight per cent of respondents said they would vote in favour of closer security ties between the EU and Switzerland, according to a survey by the GfS Bern polling and research institute.
Those rejecting the Schengen/Dublin accords account for 16 per cent, while an equal number said they had not yet made up their minds.
Previous surveys showed a similar margin between supporters and opponents of the accords.
The latest poll, which was published on Friday, was carried out in November ahead of the debates in parliament on the second set of bilateral treaties, which include the Schengen/Dublin agreement.
About 43 per cent of respondents said they would take part in a nationwide vote on the issue - a figure which is slightly above average.
Pollsters also found that most respondents do not mind if the justice minister, Christoph Blocher, voices his personal opinion on closer security cooperation with the EU.
Blocher is a member of the rightwing Swiss People’s Party, which opposes the Schengen/Dublin accord.
It has repeatedly pledged to challenge the agreements in a nationwide vote, saying they are a backdoor entrance to full EU membership.
Under the Swiss system of collegiality, the seven-member cabinet takes joint decisions and, as a rule, dissenting opinions are not made public.
The survey also revealed an increasing preference for bilateral treaties between the EU and Switzerland in the long run.
Thirty-seven per cent of respondents came out in favour – the highest number since June 2000.
Experts say the increase is the result of the successful conclusion of negotiations on the second set of bilateral accords with Brussels.
Only 17 per cent opted for Switzerland going it alone, while 23 per cent came out in favour of full EU membership, the survey said.
The GfS institute has carried out regular polls on voters’ attitude towards Europe since 1993. For the latest survey, 1,001 potential voters were interviewed.
swissinfo with agencies
68% of potential voters came out in favour of the Schengen/Dublin accords.
16% are against and 16% are undecided.
Parliament has approved the accords, but the rightwing People’s Party and far-right groups have pledged to force a nationwide vote on the issue.
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