Appearing on MSNBC's "Morning Joe," Duncan was asked by Time's Mark Halperin whether he believed it should be legal for same-sex couples to get married in the United States.
"Yes, I do," said Duncan.
When asked if he had said it publicly before, he replied that he thought that he had never been asked.
Duncan is the second cabinet secretary to publicly support same-sex marriage, with Housing and Urban Development Secretary Shaun Donovan saying last November that he "absolutely" supports it.
Biden said Sunday that he is "absolutely comfortable" with gay marriage, but added that the president sets the policy. His comments appeared to diverge from those made by President Barack Obama, who has said that he is still "evolving" on the issue.
LGBT groups quickly praised Biden, but the Obama campaign walked back his comments, with a spokesperson for the vice president saying, "The vice president was saying what the president has said previously -- that committed and loving same-sex couples deserve the same rights and protections enjoyed by all Americans, and that we oppose any effort to rollback those rights. ... Beyond that, the vice president was expressing that he too is evolving on the issue, after meeting so many committed couples and families in this country."