The poll, carried out by research institute gfs.bern and commissioned by the Swiss pharma industry, found that 77 percent considered stable relations with the EU to be important for the Swiss economy, reported news agencies on Sunday.
Around half of those surveyed said the country's raft of bilateral agreements were mostly or wholly advantageous for the country – up from 43 percent in October 2015. In contrast, only 20 percent felt the bilaterals were mostly or wholly disadvantageous.
Some 44 percent felt the bilaterals should be renegotiated and 20 percent would prefer them to be scrapped altogether, while 15 percent wanted Switzerland to join the EU.
When asked if the country should continue to collaborate with the EU based on the current bilaterals, some 78 percent said yes.
The survey will be a relief to the government, which last December chose to maintain the bilaterals rather than implement the 2014 anti-immigration initiative to the letter.
The initiative, narrowly approved by the public in a February 2014 referendum, called for quotas to be placed on immigration from the EU, in contravention of the bilateral agreement over the free movement of people.
After three years of wrangling, the Swiss government decided not to impose quotas but instead to give job preference to Swiss workers over foreign ones in certain circumstances, a hugely watered down version of the original initiative that was heavily criticized by many as an affront to democracy.
According to Sunday's survey, a slim majority (51 percent) support the government's solution, while 38 percent said they found it unsatisfactory.
However, 58 percent said the Swiss-EU bilaterals were more important than implementing the 2014 initiative to the letter.
The survey also questioned people about their support for two other popular initiatives launched in the wake of the 2014 referendum and the government's decision.
If they were to vote now, the so-called RASA initiative, which intends to repeal the 2014 anti-immigration referendum, would be rejected by a slim majority (51 percent).
Another initiative calling for the scrapping of the bilateral agreement on the free movement of people would also fail, with 58 percent voting against it and only 38 percent in favour.