Hillary Rodham Clinton had not planned to make the first major policy speech of her presidential campaign an impassioned plea to mend the nation’s racial fissures and overhaul an “out-of-balance” criminal justice system.

But by Tuesday, as the nation confronted shocking scenes of Baltimore’s smoke-filled streets, Mrs. Clinton knew that the death of Freddie Gray from injuries he suffered while in police custody would lead her to make race, poverty and incarceration of men from poor, black communities central to her early campaign.

“There is something profoundly wrong when African-American men are still far more likely to be stopped and searched by police, charged with crimes and sentenced to longer prison terms than are meted out to their white counterparts,” Mrs. Clinton said in a forceful address Wednesday at Columbia University.

She said Mr. Gray’s death, the subsequent protests and the assault on innocent police officers in Baltimore “tear at your soul.”