WASHINGTON — Hillary Rodham Clinton’s passionate speech Thursday appealing for expanded rights and opportunities for women in the U.S. and around the world wasn’t supposed to be a campaign event. But it might as well have been.

Addressing the annual Women in the World summit, Clinton made a forceful case for protecting women’s health care choices and expanding paid family leave. The front runner for the Democratic nomination, Clinton criticized “those who offer themselves as leaders” but oppose equal pay for women or want to defund Planned Parenthood — a veiled reference to some of her Republican rivals.

The speech in New York provided one of the first glimpses of how Clinton will seek to tout her gender as an asset in the 2016 campaign. Her advisers have long said they regret downplaying the history-making potential of her candidacy during her failed 2008 White House bid and have vowed to not make the same mistake this time around.

Still, that doesn’t mean Clinton herself will be talking explicitly about the prospect of being the first woman to occupy the Oval Office. She made only veiled references to her candidacy Thursday, including saying she had wanted to be at the event “regardless of what else I was doing.”

In her first two weeks as a candidate for the Democratic nomination, Clinton is instead letting her choice of events and campaign themes do the talking on the subject of a woman attaining the presidency.

During trips to Iowa and New Hampshire, that’s meant casting herself as a “champion” for American families and focusing on issues that traditionally resonate with women, like paid family leave, education and childcare. Her campaign reasons that such issues are relevant to men with families, too.

Clinton’s first events as a candidate have been small discussions with voters aimed in part at showing her softer side. She’s peppered her remarks with references to her late mother, her daughter and her infant granddaughter.

And she’s been talking directly this week, as she’s done often over the years, about rights and opportunities for women. She did so Wednesday when Georgetown University honored recipients of a prize that carries her name, the Hillary Rodham Clinton Award for Advancing Women in Peace and Security.

At the Women in the World conference, which brings together female political leaders, activists and celebrities, she said she was optimistic that women were on the brink of making important progress.

“I’m grateful that there is now a new burst of energy around the rights and opportunities of women and girls,” she said.

When Clinton first ran for president in 2008, she played down the prospect that she would be the first woman to run the country. She focused instead on her experience and grit.

That was, in part, an attempt to head off any voter concerns that a woman might not be tough enough to serve as president. It was also seen as a way to draw a contrast with Barack Obama, a freshman senator at the time.

Obama rarely talked about himself as the possible first black president during the 2008 campaign. But his supporters sometimes made that case and his team was adept at harnessing the enthusiasm of voters who were energized by his historic candidacy.

Some Clinton supporters say the former first lady may be able to do the same in the 2016 contest.

“For many voters, the chance to make history will be very important,” said Sen. Barbara Mikulski, D-Md., the longest-serving woman in the history of Congress.

Though women still trail men as political office-holders, women wield enormous power in national elections. They made up just over half of the electorate in the 2012 presidential election. About 55 percent of women backed Obama.

While Clinton will need to hold together the coalition of young people, black and Hispanic voters that also helped Obama win the White House, some Democratic strategists say she could offset some losses there by picking up a few more percentage points among women in key swing states.

To some Republicans, Clinton’s projection of a softer, more family-friendly side is simply a political ploy and an attempt to avoid talking about her record as secretary of state. Among her fiercest critics has been Carly Fiorina, the former Hewlett-Packard CEO who is the only Republican woman expected to run for president.

“She wants to make it a gender-based campaign,” Fiorina said in an interview.

Clinton’s advisers say she is simply talking about issues that are important to the middle class, and not ducking her record.

“Hillary is focused on talking with everyday Americans about the issues that impact their lives, and our nation’s future,” said Karen Finney, a spokeswoman for the campaign.