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WASHINGTON — Hillary Rodham Clinton made her public debut in her new role as prospective presidential candidate on Tuesday night by returning to the issue that has animated her long career on the national stage — the empowerment of women around the globe.

In her first public appearance since stepping down as secretary of state, Mrs. Clinton addressed a ceremony honoring women who have stood up as leaders in places like Brazil, Cambodia, Somalia and the Palestinian territories. She used the occasion to cement what she considers a central legacy of her four years as the nation’s top diplomat.

“When I became secretary of state, I was determined to weave this perspective into the fabric of American foreign policy,” Mrs. Clinton told an audience of movers and shakers at the Kennedy Center. She recalled appointing the first ambassador for global women’s rights, directing the diplomatic corps to focus on gender issues and stepping in to free a Cambodian woman jailed for protesting. “We did put women on the agenda and made it a centerpiece of all that we did.”

It was an evening without overt politics and yet Mrs. Clinton’s appearance drew attention as she enters a period of deciding whether to run for president again in 2016. Freed of her official duties and her position in President Obama’s cabinet, Mrs. Clinton began re-establishing herself as an independent figure. Her remarks were in keeping with her longstanding passions but many in the audience were rooting for her to make one more campaign to become the nation’s first female president.

Her appearance came just hours after a so-called “super PAC” formed by supporters started its Web site, ReadyforHillary.com, to support her possible candidacy and collect contributions. The super PAC, which is ostensibly independent of the would-be candidate, boasted that it already has 100,000 supporters as “part of our network.” Mrs. Clinton has also released a video endorsing same-sex marriage.

Also appearing at the event, the Vital Voices Global Leadership Awards, was Vice President Joseph R. Biden Jr., who may be her rival for the Democratic presidential nomination. The two were limited to the roles of presenting awards and they did not share a stage, although they came back out at the end together to wave to the crowd. But during her turn at the microphone, Mrs. Clinton made sure to praise Mr. Biden for championing the Violence Against Women Act, which was just reauthorized by Congress.

“I am delighted that Vice President Biden will be able to join us tonight,” Mrs. Clinton said. “Vice President Biden and I have worked together on so many important issues and one that is particularly close to his heart is the fight against domestic violence.”

When Mr. Biden appeared near the end of the event, he returned the compliment. “There’s no woman like Hillary Clinton,” he said. “That’s a fact.” He praised her “magnificent work as secretary of state,” which he said solidified the notion that “women’s issues cannot be set aside but instead must be the central project of what we’re about.”

Mr. Biden, who presented an award to the Kant brothers, founders of an organization fighting human trafficking in India, condemned the brutal treatment of girls and women in places like India and Egypt. He noted a front-page story in The New York Times about a man in Afghanistan who had agreed to give away his 6-year-old daughter in marriage to pay off a debt. “Barbaric,” he said. “Cultural norm or not, barbaric.” (A donor has now paid off his debt.)

Mr. Biden made no explicitly political comments. But he did ad-lib a joke referring to his first presidential campaign in 1988, which was sunk by plagiarism charges. Before quoting his sister, Valerie, he added to laughter, “I want to make clear I am attributing this.”

Mr. Biden had plenty of friends in the audience. But the event was effectively a coming-out party for Mrs. Clinton on home turf. Vital Voices is a nonprofit organization that seeks to identify and help women around the world to play leadership roles, an outgrowth of an initiative established in the 1990s by Mrs. Clinton when she was first lady.

So many Clinton advisers, loyalists and admirers were in the audience that Mrs. Clinton noted, “It’s a little bit like a family reunion.” Mrs. Clinton’s assignment was to offer a tribute to Melanne Verveer, her longtime friend, chief of staff while first lady, and until recently her ambassador at large for global women’s issues. Mrs. Clinton lavished praise on Ms. Verveer and warned against pessimism in the fight to empower women.

“It’s not what Melanne and I see,” she said. “When we look at the map, we do see progress.” She continued: “We see the opportunities that are there to be seized. We see, we hear those vital voices.”

“All it takes,” she added, “is for them to have a fighting chance.”