BACKGROUND: Odronextamab is a hinge-stabilised, fully human IgG4-based CD20 × CD3 bispecific antibody that binds CD3 on T cells and CD20 on B cells. We aimed to evaluate the safety and antitumour activity of odronextamab in patients with relapsed or refractory B-cell non-Hodgkin lymphoma. METHODS: This single-arm, multicentre, phase 1, dose-escalation and dose-expansion (ELM-1) trial was conducted at ten academic sites across the USA and Germany. Patients aged 18 years or older with CD20-positive relapsed or refractory B-cell malignancies who previously received CD20-directed antibody therapy and who had at least one measurable lesion, and an ECOG performance status of 0 or 1 were included. Patients received intravenous odronextamab, according to a step-up dosing schedule in cycle 1, followed by treatment once per week at target doses ranging from 0·1 mg to 320 mg during cycles 2-4 (each cycle was 21 days). After cycle 4, maintenance treatment occurred every 2 weeks until disease progression or unacceptable toxicity. The primary endpoint of safety was assessed by the incidence of adverse events and dose-limiting toxicities to determine the maximum tolerated dose or phase 2 dose of odronextamab, or both. Preliminary antitumour activity, as measured by objective response rate, was a secondary endpoint. This study is registered with ClinicalTrials.gov, NCT02290951. FINDINGS: From Feb 4, 2015, to Sept 25, 2021, 145 heavily pretreated patients (median of 3 (IQR 2-5] previous therapies) were enrolled (94 to the dose-escalation and 51 to the dose-expansion part of the study). The median age of patients was 67·0 years (IQR 57·0-73·0); 101 (70%) were male and 44 (30%) were female; most participants were White (119 [82%]) and not Hispanic or Latino (132 [91%]). 42 (29%) patients received previous CAR T therapy and 119 (82%) were refractory to the last line of therapy. Median duration of follow-up was 4·2 months (IQR 1·5-11·5). During dose escalation, odronextamab was administered up to the maximum dose of 320 mg once per week and no dose-limiting toxicities were observed. The recommended dose for expansion in patients with follicular lymphoma grade 1-3a was 80 mg and was 160 mg for patients with diffuse large B-cell lymphoma. Cytokine release syndrome and neurological treatment-emergent adverse events were predominantly low grade and did not result in treatment discontinuation. The most common grade 3 or worse treatment-emergent adverse events were anaemia (36 [25%]), lymphopenia (28 [19%]), hypophosphataemia (27 [19%]), neutropenia (27 [19%]), and thrombocytopenia (20 [14%]). Serious treatment-emergent adverse events occurred in 89 (61%) of 145 patients; the most frequent were cytokine release syndrome (41 [28%]), pyrexia (11 [8%]), pneumonia (nine [6%]), and infusion-related reaction (six [4%]). Four deaths were considered related to treatment (gastric perforation in a patient with gastric involvement by lymphoma, lung infection, pneumonia, and tumour-lysis syndrome). Objective response rate was 51% (95% CI 42-59; 72 of 142). In patients with follicular lymphoma who received odronextamab doses of 5 mg or higher, the objective response rate was 91% (95% CI 75-98; 29 of 32) and the complete response rate was 72% (95% CI 53-86; 23 of 32). In patients with diffuse large B-cell lymphoma without previous CAR T-cell therapy who received doses of 80 mg or higher, the objective response rate was 53% (eight of 15) and all responses were complete responses. In patients with diffuse large B-cell lymphoma who had previous CAR T-cell therapy and received doses of 80 mg or higher, the objective response rate was 33% (ten of 30) and complete response rate was 27% (eight of 30). INTERPRETATION: Odronextamab monotherapy showed a manageable safety profile and encouraging preliminary activity, including durable responses in heavily pretreated patients with B-cell non-Hodgkin lymphoma, supporting further clinical investigation in phase 2 and 3 trials. FUNDING: Regeneron Pharmaceuticals.