WASHINGTON — Hillary Rodham Clinton used a speech Friday on income inequality to lay out populist themes that have been increasingly embraced by the Democratic Party base whose support she would seek if she runs for president.

In the remarks, among the most specific Clinton has offered on domestic policy since she stepped down as secretary of state, she lamented the strain on the American middle class and the luxurious position of the super rich.

“For too many families in America today … the dream of upward mobility that made this country a model for the world feels further and further out of reach,” Clinton told a meeting of policymakers, journalists and academics convened by the New America Foundation. “Many Americans understandably feel frustrated, even angry,” she said.

Clinton spoke to several hundred conference participants after receiving an adulatory introduction from Google executive chairman Eric Schmidt, who chairs the board of the New America Foundation, which sponsored the two-day event, “Big Ideas for a New America.”

The event capped a week in which Clinton and her husband vigorously responded to partisan attacks, including a suggestion that she may have suffered brain damage from a fall in 2012.

As if to emphasize her vibrancy, Clinton ignored a teleprompter set up by a podium on the dais and talked directly to the audience, which interrupted her speech several times with applause.

The topic of her address also addressed another challenge Clinton faces should she run: Many Democrats have grown enthusiastic about a brand of aggressive, liberal economics championed by leaders such as Sen. Elizabeth Warren, D-Mass., and Democratic New York Mayor Bill de Blasio and not associated with Clinton or her husband.

In her New America address, Clinton cited stark statistics: More than four in 10 children born into the lowest-income families never manage to climb out of relative poverty.

“What’s more, an almost equal percentage of kids who are born into the most affluent families stay there for life no matter what their effort. That is the opposite of the mobility we think of as a hallmark of America,” she said.

Economic productivity has increased by more than 25 percent since 2000, she said, while wages for most Americans have stagnated.