A Safety and Efficacy Study of Relamorelin in Diabetic Gastroparesis Study 04

Inclusion Criteria: Two different groups of participants may enter into the study: 1. Rollover Participants Participants who were not randomization-eligible at the end of the Run-in Period of lead-in studies RLM-MD-01 (NCT03285308) or RLM-MD-02 (NCT03426345) are eligible to be randomized in the study if all of the following criteria apply: •In the lead-in studies, participants must have met all screening visit and Run-in Period criteria for randomization into the Treatment Period (including compliance with dosing, entry of diary data into the Diabetic Gastroparesis Symptom Severity Diary (DGSSD)) except that: * They had zero vomiting episodes and an average daily Diabetic Gastroparesis Symptom Severity Score (DGSSS) of ≥12 at the end of the lead-in study Run-in Period, as reported using the electronic hand-held device; OR * They had vomiting episodes and an average daily DGSSS of ≥12 but \<16 at the end of the lead-in study Run-in Period, as reported using the electronic hand-held device 2. De Novo Participants * Type 1 Diabetes Mellitus (T1DM) or Type 2 Diabetes Mellitus (T2DM) of at least 5 years' duration, with controlled and stable blood glucose levels and hemoglobin A1c (HBA1c) ≤11% * DG defined as at least a 3-month history prior to Screening of symptoms (one of which must be nausea) on an ongoing basis that are suggestive of gastroparesis (GP) (e.g., nausea, abdominal pain, postprandial fullness, bloating, vomiting, and early satiety) * Compliance with the entry of data into the hand-held electronic device during the Run-in Period * Compliance with administration of subcutaneous (SC) twice daily injections during the Run-in Period * The average of the daily DGSSS from the 2-week, Run-in Period must be ≥12 Exclusion Criteria: 1. Both Rollover and De Novo Participants •Participants with a known allergy or hypersensitivity to the study treatments and their excipients (i.e., mannitol or phenol) 2. Rollover Participants •Participants will be excluded from this study if any of the lead-in study exclusion criteria apply at the Screening Visit and at the end of the Run-in Period for randomization into the Treatment Period of studies RLM-MD-01 and RLM-MD-02, except as specified in the inclusion criteria 3. De Novo Participants * History of anorexia nervosa, binge-eating, bulimia, or other eating disorder within 5 years of the Screening Visit * History of intestinal malabsorption or pancreatic exocrine insufficiency * History of belching disorders, other nausea and vomiting disorders * Gastric or duodenal ulcer within 3 months of Screening * History of malignancy in the 3 years prior to Screening, except for adequately treated basal cell or squamous cell skin cancer, or in situ cervical cancer * Currently receiving parenteral feeding or presence of a nasogastric or other enteral tube for feeding or decompression * Use of metoclopramide, domperidone, prucalopride, macrolide antibiotics (e.g., erythromycin, clarithromycin, azithromycin), or other drugs considered to be GI promotility agents for at least 10 days prior to the start of the Run-in Period * Currently taking opiates, or expecting to use opiates during the course of the clinical study * Treatment with glucagon-like peptide-1 (GLP-1) agonist for at least 6 weeks prior to the start of the Run-in Period * History of pyloric injection of botulinum toxin within 6 months of screening * History of gastric surgery such as fundoplication, gastrectomy, gastric pacemaker placement, vagotomy, or bariatric procedure (a history of diagnostic endoscopy is not exclusionary) * Randomization in any previous study in which relamorelin was a treatment * Allergic to, or intolerant of egg, wheat, milk, or algae, as these are components of the gastric emptying breath test (GEBT) study meal