A total of 61 percent of people said they were "definitely against" or "against" the controversial initiative which would see Swiss law given priority of international law, according to the latest survey by gfs.bern and carried out in the first week of November.
That is six percentage points higher than the last gfs.bern poll from mid-October.
Meanwhile, the number of people who are either "definitely for" or "for" the initiative has fallen from 39 percent to 37 percent in the same period.
The 'Swiss law not foreign judges' initiative, also known as the ‘self-determination' initiative' (SDI) is backed by the right-wing Swiss People's Party (SVP).
With the initiative, the SVP wants the role of international law in Switzerland to be greatly reduced so that the country has more control over its own affairs.
The SVP has heavily criticised the Swiss government in recent years for failing to properly implement popular initiatives such as one against mass immigration, which was backed by voters in 2014. Despite voters backing that initiative, Bern implement a watered-down version because it would have contravened Switzerland's free movement agreement with the EU.
The SVP says the current initiative is essential to protect's Switzerland's unique system of political democracy and ensure voters's wishes are respected.
But opponents say the initiative would threaten human rights in Switzerland and create chaos in terms of Switzerland's international relations.
Under the terms of the SDI, Switzerland would be required to apply a strict mechanism to deal with conflicts between international law and the Swiss constitution. This would happen, for example, in cases where voters cast their ballots in favour of popular initiatives that contravene international law.
In such cases, Switzerland would have to try and renegotiate international treaties, and if this is not possible, it would have to pull out of them.