JACKSON, Miss.—President Donald Trump praised the achievements of the 20th-century African-American civil-rights movement and paid tribute to the movement’s martyrs as “American heroes” ahead of a museum opening Saturday, amid criticism over his past remarks on women, immigration and other issues.

“Today, we strive to be worthy of their sacrifice, we pray for inspiration from their example,” he said, after describing the life of Mississippi’s slain civil-rights leader, Medgar Evers.

“We...