Mr. Booker’s rhetorical space has been less crowded so far, but several Democrats exploring the 2020 race have been wielding similar themes. Joseph R. Biden Jr., the former vice president, and Michael R. Bloomberg, the former New York City mayor, have both extolled bipartisanship. Beto O’Rourke, the former Texas Senate candidate, told Oprah Winfrey last week that he was preoccupied with uniting “a deeply divided country.”

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It is perhaps not an accident that the most confident Democratic tribunes of good feeling are all men, while the party’s sternest warriors are mainly women. In a contest for the presidency, a position traditionally viewed in martial terms, it may be easier for a man of Mr. Biden’s backslapping swagger or Mr. Booker’s athletic stature to show tenderness or vulnerability without fear of appearing weak.

And it was with enthusiastic physicality, and regular references to having played high school and college football, that Mr. Booker preached love and understanding. He clasped his chest and his face at moments of emotion, usually stirring murmurs of appreciation and sympathy; in one case, he wrapped his arm around a voter for a midspeech selfie. While Mr. Booker said he was ready to spar with Mr. Trump, stating matter-of-factly that “there is nobody in this race tougher than me,” his overarching theme was about reconciliation.

At an airy adult learning center in Waterloo, Mr. Booker insisted that the capacity to conquer all manner of hardships was within human reach — a contrast with Ms. Warren and other populists, who tend to describe ordinary people being stripped of power by big institutions.

“The most common way people give up their power,” Mr. Booker said, “is not realizing that they have it.”

Forces of darkness appeared in Mr. Booker’s political narrative — the country, he said, has a “cancer on our soul” — but there were few villains. Where malignant people intruded, Mr. Booker leavened their presence with humor: Strom Thurmond, the South Carolina senator who embodied virulent racism, became the subject of a laughter-inducing vocal impression. Describing how a racist white real estate agent directed a dog to attack his father, Mr. Booker added a punch line: Each time his father told the story, he joked, “that dog got bigger!”