NEW YORK - Hillary Rodham Clinton formally kicked off her presidential campaign on Saturday with an enthusiastic embrace of her potential to become the first woman to win the White House, asking supporters gathered at an outdoor rally to join her in building an America "where we don't leave anyone out, or anyone behind."

With the downtown New York skyline and new World Trade Center over her shoulder, Clinton offered herself as a fierce advocate for those still struggling from the Great Recession.

She promised to carry on the liberal legacies of President Barack Obama, and former Presidents Franklin D. Roosevelt and Bill Clinton, her husband, saying "real and lasting prosperity must be built by all and shared by all."

While Clinton ended her first campaign for president in 2008 by conceding she and her backers "weren't able to shatter that highest, hardest glass ceiling," she vowed Saturday to push ahead toward an "America where a father can tell his daughter: Yes, you can be anything you want to be - even president of the United States."

"I think you know by now that I've been called many things by many people," Clinton said to cheers and laughter from the crowd of roughly 5,500 gathering on Roosevelt Island in the East River. "Quitter is not one of them."

The 67-year-old former secretary of state, first lady and Democratic senator from New York did not make her gender a core element in 2008, but it provided the cap to the first major speech of her 2016 bid.

"I will be the youngest woman president in the history of the United States. And the first grandmother as well," she said.

Two months after starting her campaign with a simple video that showed her only briefly, Clinton outlined a broad vision intended to attract the coalition of young and minority voters that propelled Obama to two victories.

In her roughly 45-minute speech, Clinton laid out a wish list of Democratic policies: universal pre-K education, increased regulation of the financial industry, paid sick leave and equal pay for women, a path to citizenship for immigrants living in the country illegally, campaign finance overhaul and a ban on discrimination against gay people and their families.

In doing so, Clinton tried to cast the 2016 election as a choice about the economic future of the middle class, saying the Republican field is "singing the same old song."

The GOP's candidates, she said, want to give Wall Street banks free reign, take away health insurance, "turn their backs" on gay people and ignore the science of climate change.

"Fundamentally, they reject what it takes to build an inclusive economy," Clinton said. "It takes an inclusive society. What I once called 'a village' that has a place for everyone."

Republicans jumped on Clinton's decision to cite her ties to Obama and were trying to raise money off the speech almost as soon as it ended. In an email appeal asking for donations, former Texas Gov. Rick Perry wrote, "We want to look toward a brighter future, not backward at the failed policies of the Obama-Clinton years."

As part of an effort to reintroduce herself to the public, Clinton stressed her career of advocacy - a calling she said was inspired by her mother's difficult upbringing.