Study to Evaluate Imetelstat (GRN163L) in Participants With International Prognostic Scoring System (IPSS) Low or Intermediate-1 Risk Myelodysplastic Syndrome (MDS)

Inclusion Criteria: * Man or woman greater than or equal to (≥) 18 years of age * Diagnosis of myelodysplastic syndrome (MDS) according to World Health Organization (WHO) criteria confirmed by bone marrow aspirate and biopsy within 12 weeks prior to Cycle 1 Day 1 (C1D1) (Phase 2) or randomization (Phase 3). In Ventricular Repolarization Substudy, diagnosis of MDS or myelodysplastic/myeloproliferative neoplasm with ring sideroblasts and thrombocytosis (MDS/MPN-RS-T) according to WHO criteria confirmed by bone marrow aspirate and biopsy within 12 weeks prior to C1D1 * International Prognostic Scoring System (IPSS) low Risk or intermediate-1 risk MDS * Red blood cell (RBC) transfusion dependent, defined as requiring at least 4 RBC units transfused over an 8-week period during the 16 weeks prior to Study Entry; pre-transfusion hemoglobin (Hb) should be less than or equal to (≤) 9.0 gram per deciliter (g/dL) to count towards the 4 units total * Eastern Cooperative Oncology Group (ECOG) performance status 0, 1 or 2 Exclusion Criteria: * Participant has known allergies, hypersensitivity, or intolerance to imetelstat sodium or its excipients * Participant has received an investigational drug or used an invasive investigational medical device within 30 days prior to Study Entry or is currently enrolled in an investigational study * Prior treatment with imetelstat sodium * Have received corticosteroids greater than (\>) 30 milligram per day (mg/day) prednisone or equivalent, or growth factor treatment within 4 weeks prior to study entry * Has received an erythropoiesis-stimulating agent (ESA) or any chemotherapy, immunomodulatory, or immunosuppressive therapy within 4 weeks prior to study entry (8 weeks for long-acting ESAs) * Phase 3: a) Prior treatment with a hypomethylating agent (example \[eg\], azacitidine, decitabine); b) Prior treatment with lenalidomide Additional Exclusion Criteria for the Ventricular Repolarization Substudy: * Concurrent therapy with medications known to prolong the QT interval and have been associated with Torsade de pointes arrhythmia (TdP) * Cardiac function abnormalities on screening ECG as follows: * Resting heart rate outside of 50 to 100 beats per minute * QT interval by Fridericia's correction method (QTcF) \>470 millisecond (msec) (or QTcF \>490 msec in the presence of a right bundle branch block or ventricular conduction delay \[QRS \>119 msec\]), determined by central assessment based on the average value of a triplicate set of ECGs * Diagnosed or suspected congenital long QT syndrome * Family history of sudden unexpected death from cardiac-related causes if indicative of a pathogenic mutation of cardiac ion channels * Family history of congenital long QT syndrome * History of Mobitz II second degree or third degree heart block * Implantable pacemaker or automatic implantable cardioverter defibrillator * Complete left bundle branch block * Chronic or persistent atrial arrhythmia including atrial fibrillation and atrial flutter * History or presence of clinically relevant heart rhythm disturbances including atrial, junctional, re-entry, and ventricular tachycardia * Unusual T-wave morphology (i.e., bifid T-wave) likely to interfere with QT measurements * History or evidence for any of the following: severe or unstable angina, myocardial infarction, symptomatic congestive heart failure, arterial or venous thromboembolic events (example, pulmonary embolism, cerebrovascular accident including transient ischemic attacks) within 12 months prior to Cycle 1 Day 1, New York Heart Association (NYHA) Class II to IV heart disease * Presence of uncontrolled hypertension (persistent systolic blood pressure \[BP\] ≥160 mmHg or diastolic BP ≥100 mmHg). Participants with a history of hypertension are permitted, provided that BP is controlled to within these limits by anti-hypertensive treatment * Any skin condition likely to interfere with electrocardiographic electrode placement or adhesion * History of thoracic surgery likely to cause abnormality of the electrical conduction through thoracic tissues