Hillary Rodham Clinton, at a major outdoor rally planned for Saturday, will directly address concerns that have emerged in the early weeks of her candidacy, telling voters they can trust her to fight for the middle class and stressing that she cares about their problems, several people briefed on her plans say.

The speech, at an event shaping up to be the most ambitious public gathering undertaken by the campaign since Mrs. Clinton began her quest for the White House in April, will be shaped by symbolism as she seeks to make the case for why she should be president.

It will be held in New York City on an island named for Franklin D. Roosevelt, in the shadow of diverse middle-class neighborhoods, as Mrs. Clinton tries to evoke the legacy of the New Deal and lay out her vision for a federal government substantially engaged in lifting American families that feel economically insecure and increasingly left behind.

And she will channel her personal hero, Eleanor Roosevelt, in emphasizing women’s and civil rights and her assertion that the Republican Party is out of touch with an increasingly diverse electorate. Her plans were described by people briefed on the speech who were not authorized to discuss it for attribution before the campaign officially released details.