Inclusion Criteria: - Subject is considered an adult according to local regulation at the time of signing informed consent. - Subject has a diagnosis of primary AML or AML secondary to myelodysplastic syndrome (MDS) or therapy-related AML according to World Health Organization (WHO) classification. - Subject has presence of the FLT3-mutated relapsed or refractory AML or FLT3-mutated AML in CRc (CR, CRi, CRp) with MRD in bone marrow or peripheral blood. [Specific to investigational sites in Japan: FLT3-mutated AML in CRc (CR, CRi, CRp) with MRD subjects will not be included.] - Subject has refractory or relapsed AML (with or without hematopoietic stem cell transplant [HSCT]) or AML in CRc (CR, CRi, CRp) with MRD by flow cytometry or genetic testing for the FLT3 mutation after induction/consolidation regimen or HSCT. [Specific to investigational sites in Japan: FLT3-mutated AML in CRc (CR, CRi, CRp) with MRD subjects will not be included.] - Subject must wait for at least 5 half-lives after stopping therapy with any investigational agent and before starting ASP2215. - Subject must meet the following criteria as indicated on clinical laboratory tests: - Serum aspartate aminotransferase (AST) and alanine aminotransferase (ALT) ≤ 3x institutional upper limit of normal (ULN) - Serum total bilirubin ≤ 2.5 mg/dL, except for subjects with Gilbert's syndrome - Serum potassium and serum magnesium ≥ institutional lower limit of normal (LLN). - Subject is able to tolerate oral administration of study drug. - Subject who has developed overall grades II-IV acute graft-versus-host disease (GVHD) must satisfy the following criteria: - No requirement of > 0.5 mg/kg of prednisone (or equivalent) daily dose within 1 week of enrollment - No escalation of immunosuppression in terms of increase of corticosteroids or addition of new agent/modality in prior 2 weeks (note that increasing calcineurin inhibitors or sirolimus to achieve therapeutic trough levels is allowed) - Female subject must either: - Be of nonchildbearing potential: - Postmenopausal (defined as at least 1 year without any menses) prior to screening, or - Documented surgically sterile (e.g., hysterectomy, bilateral salpingectomy, bilateral oophorectomy) at least 1 month prior to screening. - Or, if of childbearing potential, - Agree not to try to become pregnant during the study and for at least 180 days after the final study drug administration - And have a negative urine pregnancy test at screening - And, if heterosexually active, agree to use consistently 2 forms of effective contraception per locally accepted standards (1 of which must be a barrier method) starting at screening and throughout the study period and for at least 180 days after the final study drug administration. - Female subject must agree not to breastfeed or donate ova starting at screening and throughout the study period, and for at least 180 days after the final study drug administration. - Male subject (even if surgically sterilized) and partners who are women of childbearing potential must agree to practice 2 forms of effective contraception per locally accepted standards (1 of which must be a barrier method), starting at screening and throughout the study period and for 120 days after the final study drug administration. - Male subject must not donate sperm starting at screening and throughout the study period and for 120 days after the final study drug administration. - Subject agrees not to participate in another interventional study for AML while on treatment. - Subject who has a diagnosis of HIV may be enrolled as long as the disease is under control on antiretroviral therapy. Precautions should be taken to modify highly active antiretroviral therapy (HAART) regimen to minimize drug interactions. - There is no comparable or satisfactory alternative therapy to treat the subject's AML.

Exclusion Criteria: - Subject is eligible to participate in an ongoing clinical study of ASP2215; or has previously participated in a randomized clinical study of ASP2215 with a primary endpoint of overall survival that is not closed for efficacy. - Subject with QTcF > 450 ms at screening based on local reading. - Subject with a known history of Long QT Syndrome at screening. - Subject was diagnosed with acute promyelocytic leukemia (APL). - Subject has BCR-ABL-positive leukemia (chronic myelogenous leukemia in blast crisis). - Subject has clinically significant coagulation abnormality unless secondary to AML. - Subject has active hepatitis B or C or an active hepatic disorder. - Subject has uncontrolled angina, severe uncontrolled ventricular arrhythmias, electrocardiographic evidence of acute ischemia, or New York Heart Association (NYHA) Class IV heart failure. - Subject requires treatment with concomitant drugs that are strong inducers of CYP3A. - Subject has any condition which makes the subject unsuitable for study participation. - Subject has hypersensitivity to any of the study drug components.