Inclusion Criteria:  Patient is male or female aged ≥18 years. Patient provided signed and dated informed consent prior to initiation of any study procedures. Patient has relapsed AML after complete remission of any duration as evidenced by presence of neoplastic blasts in the bone marrow confirmed by flow cytometry OR has refractory AML, defined as primary refractory to at least 2 cycles of induction therapy. No other therapy exists or patient has received all standard therapies that would be potentially curative or might provide significant benefit. Patient has an Eastern Cooperative Oncology Group performance status (ECOG PS) of 0, 1, or 2. Patient has a predicted life expectancy of ≥3 months. Patient has a total white blood cell count of count ≤ 25.0 x 10^9/L at screening and on C1D1. (Patient may have received hydroxyurea prior to the screening sample for elevated WBC but must have discontinued the therapy at least 72 hours prior to screening, and not be treated with hydroxyurea after the screening sample has been taken). Patient has adequate renal function (creatinine ≤2 × the upper limit of the normal range (ULN) and an estimated glomerular filtration rate (eGFR) of >30 mL/min/1.73 m^2).  Patient has adequate hepatic function, as evidenced by a total bilirubin ≤2 × ULN, aspartate aminotransferase (AST) ≤5 × ULN and /or alanine aminotransferase (ALT)  ≤5 × ULN, unless due to leukemia involvement in the judgement of the Principal Investigator in consultation with the Medical Monitor.  Patient has adequate cardiac function with an ejection fraction (EF) ≥45%, as assessed by multi-gated acquisition (MUGA) or ultrasound/echocardiography (ECHO) and corrected QT interval by Fridericia's correction formula (QTcF) <450 msec for males and <470 msec for females. The eligibility of patients with ventricular pacemakers for whom the QT interval may not be accurately measurable will be determined on a case-by-case basis by the Sponsor in consultation with the Medical Monitor.  Patient and his/her partner agree to use adequate contraception after providing written informed consent through 3 months after the last dose of fosciclopirox, as follows:  For women: Negative pregnancy test during Screening and at Day 1 of each treatment cycle and compliant with a medically-approved contraceptive regimen during, and for 3 months after, the Treatment period or documented to be surgically sterile or postmenopausal. For men: Compliant with a medically-approved contraceptive regimen during, and for 3 months after, the Treatment period or documented to be surgically sterile. Men whose sexual partners are of child-bearing potential must agree to use 2 methods of contraception prior to study entry, during the study, and for 3 months after the Treatment period. Men must also agree not to donate sperm during the Treatment period and for 3 months after the Treatment period. Patient is willing and able to participate in the study and comply with all study requirements. Prior allogeneic stem cell transplant is allowed as long as patient is more than 100 days post-transplant and has no active graft versus host disease.  Exclusion Criteria:  Patients who meet any of the following exclusion criteria are not to be enrolled in this study.  Patient has another active malignancy. Patient has acute promyelocytic leukemia (APL) or Ph+ AML. Patient has total white blood cell count >25.0 x 10^9/L at C1D1. Patient has clinically significant cardiac disease. Patient has known chronic active liver disease or evidence of acute or chronic Hepatitis B Virus (HBV) or Hepatitis C (HCV). Patient has known diagnosis of human immunodeficiency virus (HIV) infection. Testing is not required in absence of clinical suspicion. Patients has any serious and/or uncontrolled concurrent medical conditions (e.g., uncontrolled infection, uncontrolled diabetes) or psychiatric illness that could, in the investigator's opinion, cause unacceptable safety risks or potentially interfere with the completion of the treatment according to the protocol. Patient has received any live viral vaccine used for prevention of infectious diseases within 4 weeks prior to Baseline. If female, patient is pregnant or breast-feeding. Patient is taking warfarin. Patient has known allergy or hypersensitivity to any component of fosciclopirox. Patient is taking any iron replacement therapy administered IV, intramuscularly, or orally due to the potential for loss of anticancer activity due to drug and/or metabolites chelating iron. Patient is taking Hydrea (hydroxyurea) within 72 hours prior to the screening visit.