At a donor meeting in the Red Hook, Brooklyn, last week, Mrs. Clinton raised the topic as she addressed more than 250 people who had helped raise at least $27,000 for her 2016 presidential campaign, according to three people who attended the gathering.

“We’re going to make clear, I’m not running for my husband’s third term or for President Obama’s third term,” one person recalled her saying. “I’m running to make history on my own.”

Later, all three attendees said, she talked about the campaign being not about her, but about voters, and said she wanted to build on the successes of both Mr. Obama and Mr. Clinton.