Gays, lesbians and transgender people "are our colleagues, our teachers, our soldiers, our friends, our loved ones. And they are full and equal citizens and deserve the rights of citizenship - that includes marriage", she said Monday in a statement some saw as an indication of her possible candidacy for president in 2016.
Clinton, 65, made repeated references during the roughly six-minute-long video to her work as secretary of state during which she promoted LGBT rights as an important part of US foreign policy.
A survey by the Pew Center showed that 46 percent of voters in the 2012 elections favoured legal status for same-sex couples, while 44 percent were opposed.
But with a view to the future, the poll showed that support for same-sex marriages reaches 59 percent among citizens born between 1980 and 2000.
Other possible competitors for the 2016 Democratic presidential nomination, such as Vice President Joe Biden, Maryland Gov. Martin O'Malley and New York Gov. Andrew Cuomo, also support the right of same-sex couples to marry.