WASHINGTON — In a forceful speech on Saturday to an influential gay rights group, Hillary Rodham Clinton reaffirmed her support for gay, lesbian, bisexual and transgender Americans.

Hours later, Vice President Joseph R. Biden Jr., who is contemplating his own presidential run, stood before the same organization and praised Americans who have fought for gay rights.

“Love is not a political matter; it’s a basic human right,” Mr. Biden said to a gathering of members of the Human Rights Campaign on Saturday night. “The fact that we recognize that, it’s because of you.”

Mr. Biden’s potential candidacy has loomed over Mrs. Clinton’s campaign, and the speeches on Saturday presented a rare occasion for these two former Senate colleagues and potential rivals to showcase their zeal and style on gay rights, one of the most galvanizing issues for Democratic primary voters and donors.