A poll conducted by the Léger institute found that 54 percent of respondents favoured same-sex marriage, although a majority of men were opposed.
The findings were published by the German-language SonntagsBlick.
The results showed that 62 percent of women supported gay marriage, compared to 46 percent of men.
Another survey, conducted by gfs-Zurich and published by SonntagsZeitung, found that 71 percent of respondents were favourable or “somewhat favourable” to same-sex marriage.
The opinion poll was commissioned by Pink Cross, the Swiss organization for gays.
The full results of the survey will be published in March.
Both polls involved interviews with around 1,000 people.
While Switzerland has recognized same-sex couples since 2007, same-sex marriage is not yet legal.
However, on Friday the law committee of the lower house of parliament voted in favour of homosexual marriage.
Any move to legalize such unions would require a change to the Swiss constitution and the approval of Swiss citizens in a national referendum.