Mr. Biden’s forceful — and somewhat exaggerated — remarks, made at an event focused on voters of color, reflected the intensifying competition between Mr. Biden and Senator Bernie Sanders of Vermont here in the leadoff caucus state, as well as the importance of substantial African-American support to Mr. Biden’s campaign. In fact, in some polls Mr. Sanders does hold an advantage among younger African-American voters, and, while Mr. Biden maintains a significant lead among black voters over all, the margin varies from survey to survey and has tightened in some polls.

Mr. Biden’s fate in Iowa remains uncertain amid a fluid race less than two weeks before the caucuses, but he has always been sure of his strength in the states with larger black populations that vote after Iowa and New Hampshire, especially South Carolina. And so, when Ms. Hylton suggested that his lead was slipping amid a Sanders rise, citing a Vice News poll, Mr. Biden protested vigorously.

“But he’s way behind me,” he said. “He’s way behind.”

(A Vice News-Ipsos poll associated with the forum was conducted online.)

Throughout the forum, Mr. Biden was stern, passionate and sometimes combative as he discussed his standing with black voters.

He fiercely asserted his ability to connect with African-American people. (“I’m not saying, ‘I am black,’” he said. “But I want to tell you something. I have spent my whole career with the black community.”) He described his empathy for black Americans and said he had “never, ever, ever, ever” taken their votes for granted, “not once.” And he hinted at disdain for “especially young reporters” who, according to Mr. Biden, wonder why so many African-Americans like him.