The purpose of this study is to evaluate the efficacy and safety of imetelstat sodium in transfusion-dependent participants with low or intermediate-1 risk myelodysplastic syndrome (MDS) that is relapsed/refractory to erythropoiesis-stimulating agent (ESA) treatment in Phase 2 study and to compare the efficacy, in terms of red blood cell (RBC) transfusion independence (TI), of imetelstat sodium to placebo in transfusion-dependent participants with low or intermediate-1 risk MDS that is relapsed/refractory to ESA treatment in Phase 3 study. A separate Ventricular Repolarization Substudy (QTc Substudy) will evaluate the effect of imetelstat sodium on ventricular repolarization. An Extension Phase has been included to allow continued treatment for those participants who are benefitting from imetelstat sodium and to continue to evaluate the long-term safety, overall survival (OS), and disease progression, including progression to acute myeloid leukemia (AML) in transfusion-dependent participants with low or immediate-1 risk MDS that is relapsed/refractory to ESA treatment.