ENLARGE Democratic presidential candidate Hillary Clinton spoke at an NAACP dinner in Detroit on Sunday. Photo: Rebecca Cook/Reuters

DETROIT—Hillary Clinton blasted Republican Donald Trump on race and equality issues Sunday, warning that the progress made on President Barack Obama’s watch could be wiped away if the businessman is elected president.

At an NAACP event, the Democratic front-runner offered reminders of Mr. Trump’s involvement in the “insidious birther movement” and his efforts to discredit Mr. Obama’s citizenship.

“When he was asked in a national television interview to disavow David Duke and other white supremacists who are supporting his campaign, he played coy,” Mrs. Clinton said of Mr. Trump. “We cannot let Barack Obama’s legacy fall into Donald Trump’s hands.”

Since launching his presidential campaign, Mr. Trump has had little to say about his role in the “birther” effort and his previous demands to see Mr. Obama’s birth certificate. He sparked outrage in February when he declined to distance himself from Mr. Duke, a former Ku Klux Klan leader. Mr. Trump eventually blamed a “bad earpiece” used in a TV interview and then disavowed the white nationalist.

Mrs. Clinton resurfaced those remarks Sunday as she continued to ramp up her attacks on the Republican real-estate mogul while casting herself as the president’s most ardent defender. Mrs. Clinton returned to Michigan eight weeks after suffering an unexpected defeat at the hands of Vermont Sen. Bernie Sanders in the state’s Democratic primary. But on Sunday night, she attracted a friendly crowd of several thousand who cheered her promises to tackle racism, improve educational opportunities and overhaul the criminal justice system.

“Race still plays a significant role in determining who gets ahead in America and who gets left behind,” Mrs. Clinton said. “I want you to know I get it and I see it.… For many white Americans, it’s tempting to believe that systemic racism is largely behind us.”

Campaigning in Detroit two days ahead of Indiana’s Democratic primary, Mrs. Clinton made no mention of Mr. Sanders and instead focused her fire on Republicans.

“We’ve got some candidates in this race who are trying to divide us,” she said. “We’ve got some candidates in this race who are stoking hatred and inciting violence.”