David Cameron says the Bill, introduced again today to the Commons for its third reading, would help build a stronger and fairer society. It also has the backing of Deputy Prime Minister Nick Clegg and Labour Leader Ed Miliband.
But there is opposition from some Conservative activists and MPs.
Mr Paterson is defying ministerial convention by opposing the Bill. He is set to vote for a series of amendments that would permit teachers, faith schools and registrars to opt out of marrying gay men and lesbians.
He said today: "I voted against it at the second reading and I will vote against it at the third reading.
"It's simple – marriage should be between a man and a woman."
See also: MPs to debate gay marriage plans