Hillary Clinton has said the US criminal justice system is "out of balance" and she supports federal reviews of police-involved deaths of unarmed black men in Ferguson, Missouri, and New York.
Mrs Clinton said the two cases, which have stirred a national conversation on race and law enforcement, show the need for federal funds to be used for best practices, "rather than weapons of war".
The former first lady is the leading Democratic contender to succeed President Barack Obama should she seek the presidency again.
Mr Obama is the nation's first black president, and the two cases could shape how Mrs Clinton talks about civil rights and seeks to maintain support among African-American voters, a key Democratic constituency.
Mrs Clinton's remarks at a women's conference in Boston were the first time she has spoken about the two cases in the aftermath of findings by grand juries and racially charged protests around the nation.
Civil rights leaders have criticised the grand jury decisions not to charge a white police officer over the chokehold death of Eric Garner in New York and a separate decision not to charge a white officer who shot and killed 18-year-old Michael Brown in Missouri.
Mrs Clinton, a former secretary of state, said the families and communities deserved a "full and fair accounting" and the deaths had forced the nation to "grapple with some hard truths about race and justice in America".
She noted that black men are more likely to be stopped and searched by police, charged with crimes and sentenced to longer prison terms.
"We have allowed our criminal justice system to get out of balance," Mrs Clinton said. "And I personally hope that these tragedies give us the opportunity to come together as a nation to find our balance again."
At the Massachusetts Conference for Women, Mrs Clinton expressed support for reviews by the Justice Department and Mr Obama's recent announcement of a task force on policing.