Gay marriage backed by George Osborne and William Hague
The foreign secretary and chancellor have both said they will back the introduction of same-sex marriage when MPs are given a free vote on the issue.
The comments from George Osborne and William Hague came as a poll suggested most grassroot party members want the prime minister to drop the plans.
Mr Osborne said the party supported "institutions of commitment" and Mr Hague said the plans were "right".
The Church of England and other religious groups oppose the proposals.
Under the proposals - outlined in a consultation earlier this year - religious organisations would not be obliged to conduct same-sex marriages in their places of worship and there would be no change to how religious marriages are solemnized.
Prime Minister David Cameron, deputy PM Nick Clegg and Labour leader Ed Miliband are all also in favour of legalising gay marriage in England and Wales.
Speaking on Sky News, Mr Osborne said: "I support gay marriage. I support gay marriage because I believe Conservatives support the institutions of commitment."
End Quote Colin Hart Coalition for Marriage
What this latest poll reflects is the growing unease amongst grassroot Conservatives”
Mr Hague said: "I will support the prime minister's position... This is for every MP to decide for themselves and I think that is the right position on a conscience issue."
The comments came as the Coalition for Marriage campaign group released the results of a ComRes survey on the eve of the Conservative Party conference, which was conducted among about a sixth of constituency chairmen.
The random sample of 100 chairmen indicated that 71% think the policy should be abandoned, while 47% believe Mr Cameron's stance on the issue had cost the party members.
Colin Hart, the coalition's campaign director of the campaign group said: "What this latest poll reflects is the growing unease amongst grassroot Conservatives about the way the PM is trying to force through this policy without any electoral mandate and without any acknowledgement of the profound consequences this change will have."
Meanwhile, former shadow home secretary David Davis told a conference fringe event: "Gay marriage is an issue for the church, not the state."
Same-sex couples have been able to enter into civil partnerships, which confer broadly similar rights and responsibilities to married couples, since 2005.
The Scottish government has also said it will seek to legislate to introduce gay marriage by 2015, which has sparked a fierce row with the Roman Catholic Church in Scotland.