“We’re reaching out, but it’s no secret that Bernie represents a state that is heavily Caucasian, and his decades of work on issues of importance to African-Americans aren’t known amid the national conversation on race that is underway,” said Jeff Weaver, Mr. Sanders’s campaign manager. “I don’t think it’s presumptuous of him to speak out on these issues. And his message — the need for more good-paying jobs, and opening up higher education regardless of wealth and family background — will have strong appeal with African-Americans and many other voters.”

The challenge facing Mr. Sanders as a Ben & Jerry’s candidate seeking the nomination of President Obama’s party was on vivid display last month in Burlington, Vt., at his first campaign rally.

Nearly all the speakers who preceded him — including the two ice cream entrepreneurs — were white, as were nearly all the supporters, many of them in tie-dyed clothes, who packed a park on the shores of Lake Champlain. His jeremiads about campaign-finance overhaul and climate change inspired cheers and ovations. But he made no mention of problems of deep concern to many African-Americans, like policing, gun control, racial inequities or the high numbers of black men in prison.

“The Bernie Sanders voter is still a Volvo-driving, financially comfortable liberal who is pretty much white,” said Paul Maslin, a pollster who worked for the 2004 presidential campaign of Vermont’s last Democratic contender, Howard Dean. “I don’t see how Bernie takes large numbers of black voters away from Hillary Clinton, and he needs to if he wants any shot at the nomination.”

David Axelrod, formerly Mr. Obama’s chief strategist, noted that insurgent Democrats like Gary Hart and Mr. Dean who were able to win over many white voters fell short because they could not attract blacks.