Scotland for Marriage, which is backed by various religious groups, including the Catholic Church, instructed an independent poll on the fiercely debated topic in January.
It claims the results show most Scots (53%) do not think marriage should be redefined to include same-sex relationships.
However, the Equality Network in Scotland has criticised the poll, claiming it was "imbalanced".
Tim Hopkins, Equality Network director, said: "In any opinion poll, the wording of the questions has a big influence on the results. It looks like the main question here was worded something like 'since same-sex couples already have the same rights as married couples available to them under civil partnership, should they be allowed to redefine marriage for everyone else?'.
"It is a highly leading and biased question, wrongly stating that the proposal will redefine marriage for everyone else. It won't. "
Mr Hopkins claimed that the Scottish Social Attitudes Survey, carried out by the Scottish Government in 2010 was clearer as it asked: "Do you agree or disagree that gay or lesbian couples should be allowed to marry?" At that point, 61% agreed and 19% disagreed.
Catholic Church spokesman Peter Kearney defended the survey, claiming it was a "professional and properly conducted poll". He said: "The wordings were carefully vetted by the polling company. They are not leading questions, they are perfectly fair and reasonable questions."