Defence Secretary Philip Hammond said there was a "real sense of anger" among voters over the government's plans to allow same-sex marriages.
Mr Hammond said the government's legislation to allow gay weddings would have upset "vast numbers of people."
He told BBC1's Question Time: "I have just never felt that this is what we should be focusing on. This change does redefine marriage.
"For millions and millions of people who are married, the meaning of marriage changes.
"There is a real sense of anger among many people who are married that any government thinks it has the ability to change the definition of an institution like marriage."