Washington addressed reporters at Minneapolis City Hall with her and Floyd's daughter, Gianna, beside her.
The death last week of Floyd, an unarmed black man, as a white police officer in Minneapolis pressed his knee into Floyd's neck, unleashed a wave of outrage in cities around the United States about the treatment of black Americans, further polarizing a country politically and racially.
The demonstrations have been largely peaceful but have turned violent in many cities after dark, with some violent clashes between protesters and authorities.