Vice President Kamala Harris used her acceptance speech at the Democratic National Convention on Thursday to present herself as a pragmatic leader who could unite all Americans behind a “new way forward,” painting her opponent, former President Donald J. Trump, as a dangerous and “unserious man” whose election would alter the foundation of American democracy.

With a steady voice and a straightforward gaze, Ms. Harris, a former prosecutor, presented the lengthiest and most serious case she has made against Mr. Trump as a presidential candidate.

At each turn of the nearly 40-minute address, Ms. Harris warned that the former president’s truculent behavior belied a serious and substantive threat to Americans, whether they are seeking access to reproductive health care, concerned about the safety and stability of diplomatic relationships or worried about the flow of immigrants across the nation’s southern border.

“With this election, our nation has a precious, fleeting opportunity to move past the bitterness, cynicism and divisive battles of the past,” she said. “A chance to chart a new way forward. Not as members of any one party or faction, but as Americans.”

Speaking to thousands of supporters at the United Center in Chicago, Ms. Harris acknowledged that her candidacy was not the one her party was expecting as little as a few weeks ago. But she told the crowd that she was “no stranger to unlikely journeys,” describing herself as the daughter of an Indian scientist whose dreams of a new life in the United States became the catalyst for Ms. Harris’s legal and political career. Her mother, she said wryly, taught her to “never do anything half-assed.”

Although she didn’t mention it, Ms. Harris’s nomination is barrier-breaking: She is the first Black woman and first person of South Asian descent to accept a major party’s nomination. If elected, she would be the first female president in the nation’s history.