Background Internal tandem duplication mutations in FLT3 are common in acute myeloid leukaemia and are associated with rapid relapse and short overall survival. The clinical benefit of FLT3 inhibitors in patients with acute myeloid leukaemia has been limited by rapid generation of resistance mutations, particularly in codon Asp835 (D835). We aimed to assess the highly selective oral FLT3 inhibitor gilteritinib in patients with relapsed or refractory acute myeloid leukaemia. Methods In this phase 1–2 trial, we enrolled patients aged 18 years or older with acute myeloid leukaemia who either were refractory to induction therapy or had relapsed after achieving remission with previous treatment. Patients were enrolled into one of seven dose-escalation or dose-expansion cohorts assigned to receive once-daily doses of oral gilteritinib (20 mg, 40 mg, 80 mg, 120 mg, 200 mg, 300 mg, or 450 mg). Cohort expansion was based on safety and tolerability, FLT3 inhibition in correlative assays, and antileukaemic activity. Although the presence of an FLT3 mutation was not an inclusion criterion, we required ten or more patients with locally confirmed FLT3 mutations (FLT3mut+) to be enrolled in expansion cohorts at each dose level. On the basis of emerging findings, we further expanded the 120 mg and 200 mg dose cohorts to include FLT3mut+ patients only. The primary endpoints were the safety, tolerability, and pharmacokinetics of gilteritinib. Safety and tolerability were assessed in the safety analysis set (all patients who received at least one dose of gilteritinib). Responses were assessed in the full analysis set (all patients who received at least one dose of study drug and who had at least one datapoint post-treatment). Pharmacokinetics were assessed in a subset of the safety analysis set for which sufficient data for concentrations of gilteritinib in plasma were available to enable derivation of one or more pharmacokinetic variables. This study is registered with ClinicalTrials.gov, number NCT02014558, and is ongoing. Findings Between Oct 15, 2013, and Aug 27, 2015, 252 adults with relapsed or refractory acute myeloid leukaemia received oral gilteritinib once daily in one of seven dose-escalation (n=23) or dose-expansion (n=229) cohorts. Gilteritinib was well tolerated; the maximum tolerated dose was established as 300 mg/day when two of three patients enrolled in the 450 mg dose-escalation cohort had two dose-limiting toxicities (grade 3 diarrhoea and grade 3 elevated aspartate aminotransferase). The most common grade 3–4 adverse events irrespective of relation to treatment were febrile neutropenia (97 [39%] of 252), anaemia (61 [24%]), thrombocytopenia (33 [13%]), sepsis (28 [11%]), and pneumonia (27 [11%]). Commonly reported treatment-related adverse events were diarrhoea (92 [37%] of 252]), anaemia (86 [34%]), fatigue (83 [33%]), elevated aspartate aminotransferase (65 [26%]), and increased alanine aminotransferase (47 [19%]). Serious adverse events occurring in 5% or more of patients were febrile neutropenia (98 [39%] of 252; five related to treatment), progressive disease (43 [17%]), sepsis (36 [14%]; two related to treatment), pneumonia (27 [11%]), acute renal failure (25 [10%]; five related to treatment), pyrexia (21 [8%]; three related to treatment), bacteraemia (14 [6%]; one related to treatment), and respiratory failure (14 [6%]). 95 people died in the safety analysis set, of which seven deaths were judged possibly or probably related to treatment (pulmonary embolism [200 mg/day], respiratory failure [120 mg/day], haemoptysis [80 mg/day], intracranial haemorrhage [20 mg/day], ventricular fibrillation [120 mg/day], septic shock [80 mg/day], and neutropenia [120 mg/day]). An exposure-related increase in inhibition of FLT3 phosphorylation was noted with increasing concentrations in plasma of gilteritinib. In-vivo inhibition of FLT3 phosphorylation occurred at all dose levels. At least 90% of FLT3 phosphorylation inhibition was seen by day 8 in most patients receiving a daily dose of 80 mg or higher. 100 (40%) of 249 patients in the full analysis set achieved a response, with 19 (8%) achieving complete remission, ten (4%) complete remission with incomplete platelet recovery, 46 (18%) complete remission with incomplete haematological recovery, and 25 (10%) partial remission Interpretation Gilteritinib had a favourable safety profile and showed consistent FLT3 inhibition in patients with relapsed or refractory acute myeloid leukaemia. These findings confirm that FLT3 is a high-value target for treatment of relapsed or refractory acute myeloid leukaemia; based on activity data, gilteritinib at 120 mg/day is being tested in phase 3 trials. Funding Astellas Pharma, National Cancer Institute (Leukemia Specialized Program of Research Excellence grant), Associazione Italiana Ricerca sul Cancro.