The Conservative group backing gay marriage was formed by Nick Herbert, the former police minister who resigned from the Government in September's reshuffle.
Mr Herbert, who is in a civil partnership, said changing the law was "the right the thing to do".
He said: "It is precisely because marriage is such a uniquely important institution that we should ensure that all couples who want to enter into it, regardless of their sexuality, can do so. Conservatives who believe in marriage should feel this most strongly."
However, Mr Herbert insisted it would be wrong to "compel religious organisations to marry same-sex couples against their will" and called for legal "safeguards" to prevent it.
Same-sex marriage will remain illegal in the Church of England, as the Government unveiled its plans to extend marriage to gay couples.
David Cameron is facing a backlash from Tory MPs and religious groups over allowing gay weddings in churches.