Inclusion Criteria:

          -  Subject has morphologically documented primary or secondary AML by the World Health
             Organization (WHO) criteria (2008) which is relapsed or refractory after failing at
             least 1 regimen and is not a candidate for established salvage treatment regimens. For
             expansion cohorts, patients are eligible if they have had ≤ 3 prior lines of therapy.
             Lines of therapy include initial induction (up to 2 cycles) with
             consolidation/maintenance, if applicable, and subsequent salvage regimens.
             Consolidation alone and stem cell transplantation are not counted as lines of therapy.

          -  Subject has an Eastern Cooperative Oncology Group performance score (ECOG) ≤ 2

          -  Subject has adequate renal function with an estimated creatinine clearance of ≥ 30
             mL/min by the Cockcroft-Gault equation adjusted for body weight

          -  Subject has a total bilirubin ≤ 1.5 x upper limit of normal (ULN), albumin ≥ 2.5 g/d,
             aspartate aminotransferase (AST) and alanine aminotransferase (ALT) ≤ 2.5 x upper
             limit of normal (ULN)

          -  Subjects must be competent to comprehend, provide written informed consent, and date
             an independent ethics committee/institutional review board/research ethics board
             (IEC/IRB/REB) approved informed consent form

          -  A female subject is eligible to participate if she is not pregnant and at least one of
             the following conditions applies:

               -  Not a woman of childbearing potential (WOCBP) OR

               -  WOCBP who agrees to follow the contraceptive guidance throughout the treatment
                  period and for at least 6 months after the final study drug administration.

          -  Female subject must agree not to breastfeed starting at screening and throughout the
             study period, and for 6 months after the final study drug administration.

          -  Female subject must not donate ova starting at screening and throughout the study
             period, and for 6 months after the final study drug administration.

          -  A male subject with female partner(s) of child-bearing potential must agree to use
             contraception during the treatment period and for at least 6 months after the final
             study drug administration.

          -  A male subject must not donate sperm during the treatment period and for at least 6
             months after the final study drug administration.

          -  Male subject with a pregnant or breastfeeding partner(s) must agree to remain
             abstinent or use a condom for the duration of the pregnancy or time partner is
             breastfeeding throughout the study period and for 6 months after the final study drug
             administration.

        Exclusion Criteria:

          -  Subject has a diagnosis of acute promyelocytic leukemia (APL)

          -  Subject has preexisting sensory or motor neuropathy Grade ≥ 2 at baseline

          -  Subject has received small molecule therapy, radiotherapy, immunotherapy, monoclonal
             antibodies, investigational drug, or chemotherapy within 14 days before first dose of
             study drug, with the exception of hydroxyurea

          -  Subject has any Grade ≥ 2 persistent non-hematological toxicity related to
             allotransplant

          -  Subject with Graft vs. Host Disease (GVHD) who is receiving treatment with systemic
             glucocorticoids > 10 mg/day equivalent of prednisone; however, treatment with low dose
             glucocorticoids (≤ 10 mg/day equivalent of prednisone) is permitted

               -  The use of systemic glucocorticoids in excess of 10 mg/day equivalent of
                  prednisone is permitted provided it is not for the treatment of GVHD (e.g.
                  chronic obstructive pulmonary disease, anti-emetic, infusion reactions). The
                  chronic use of topical, inhaled, and locally injected steroids is permitted

          -  Subject has known current central nervous system (CNS) disease

          -  Active angina or Class III or IV Congestive Heart Failure (CHF) (New York Heart
             Association CHF Functional Classification System) or clinically significant cardiac
             disease within 12 months of the first dose of study drug, including myocardial
             infarction, unstable angina, Grade 2 or greater peripheral vascular disease,
             congestive heart failure, uncontrolled hypertension, or arrhythmias not controlled by
             medication

          -  Subject has clinical evidence of Disseminated Intravascular Coagulation

          -  Subject has known positivity for human immunodeficiency virus

          -  Subject has known active hepatitis B (positive hepatitis B surface antigen [HBs Ag])
             or C infection. For subjects who are negative for HBs Ag, but hepatitis B core
             antibody (HBc Ab) positive, an HB deoxyribonucleic acid (DNA) test will be performed
             and if positive, the subject will be excluded. Subjects with positive serology but
             negative hepatitis C virus (HCV) ribonucleic acid (RNA) test results are eligible.

          -  Subject has an uncontrolled active infection requiring treatment and grade 3 or higher
             fever 48 hours before the first dose of study drug. Controlled infections (i.e. 3
             negative cultures completing antibiotics and/or stable fungal infection in therapy)
             are allowed provided the subject has a temperature of < 38.3°C within 48 hours of the
             first dose of study drug.

          -  Subject has a known sensitivity to any of the components of the investigational
             product ASP1235 (AGS62P1):

               -  ASP1235 (AGS62P1)

               -  L-Histidine base

               -  L-Histidine HCl

               -  α, α -Trehalose Dihydrate

               -  Polysorbate 20

          -  Major surgery within 28 days of the first dose of study drug

          -  Subject is pregnant or lactating

          -  Subject has a condition or situation which may put the subject at significant risk,
             may confound the study results, or may interfere significantly with subject's
             participation in the study

          -  Subject has any medical, psychiatric, addictive or other disorder which compromises
             the ability of the subject to give written informed consent and/or to comply with
             procedures

          -  Subject has ocular condition such as:

               -  Active infection or corneal ulcer

               -  Monocularity

               -  History of corneal transplantation

               -  Contact lens dependent (if using contact lens, must be able to switch to glasses
                  during the entire study duration)

               -  Uncontrolled glaucoma (topical medications allowed)

               -  Uncontrolled or active ocular problems (e.g., retinopathy, macular edema, active
                  uveitis, macular degeneration) requiring surgery, laser treatment, or
                  intravitreal injections

               -  Papilledema or other active optic nerve disorder