Two-thirds of Scots believe religious organisations should have the right to decide whether to conduct same-sex marriages.
A poll also found 64% now support same-sex marriage. The Scottish Government is due to publish the results of its consultation on the issue this month.
Ipsos Mori found 68% of the 1003 people asked agreed that religious organisations should be able to marry same-sex couples if they want to.
The Scottish Government launched its public consultation stating it "tends towards the view" that same-sex marriage should be introduced but that faith groups and their celebrants should not be obliged to solemnise the ceremonies.
The Scotland for Marriage group, which is supported by some religious groups, has campaigned against the proposal, while the Faith in Marriage campaign - a coalition including, among others, the United Reformed Church, the Quakers, Buddhists and the Pagan Federation - has spoken out in support.
Tom French, policy co-ordinator for the Equality Network, said: "Scotland has spoken and the message is clear; there is now overwhelming support for equal marriage across the country and in the Scottish Parliament.
"This record level of support gives the Scottish Government the green light they need to announce legislation that will give lesbian, gay, bisexual and transgender people full marriage equality; both civil and religious."
The poll was conducted on behalf of the Equality Network, LGBT Youth Scotland and the Scottish Youth Parliament.
Last week, the Equality Network announced that 69 MSPs had signed its pledge saying they would back a change in the law.
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