Inclusion Criteria:

• Have a projected life expectancy of at least 12 weeks, as assessed by the Investigator.
• Have histological confirmation of AML by World Health Organization (WHO) 2016 criteria and are either:
  • refractory to intensive induction chemotherapy; OR
  • relapsed after intensive induction chemotherapy or stem cell transplant; OR
  • relapsed after or refractory to treatment with molecularly targeted and/or low-intensity chemotherapeutic regimens.
• Have an Eastern Cooperative Oncology Group (ECOG) Performance status of 0 to 2.
• Have adequate renal function as demonstrated by measured or calculated creatinine clearance ≥ 60 mL/min.
• Have adequate liver function as demonstrated by:
  • Aspartate aminotransferase (AST) ≤ 2.5 × upper limit of normal (ULN);
  • Alanine aminotransferase (ALT) ≤ 2.5 × ULN;
  • Bilirubin ≤ 1.5 × ULN - unless considered due to leukemic organ involvement.
• Women of child-bearing potential (according to recommendations of the Clinical Trial Facilitation Group [CTFG]) must not be pregnant or breastfeeding and must have a negative pregnancy test at screening.

Exclusion Criteria:

• Poor medical risk in the investigator's opinion because of systemic diseases in addition to the cancer under study, for example, uncontrolled infections.
• Known clinically active central nervous system (CNS) leukemia.
• BCR-ABL-positive leukemia (chronic myelogenous leukemia in blast crisis).
• Diagnosis of acute promyelocytic leukemia (M3 AML or APML).
• Second malignancy currently requiring active therapy, except breast or prostate cancer stable on or responding to endocrine therapy.
• Graft Versus Host Disease (GVHD), or any GVHD requiring treatment with immunosuppression. Any GVHD treatment (including calcineurin inhibitors) must be discontinued at least 28 days prior to Day 1 of study treatment.
• Presence of persistent toxicities of Grade > 1 from prior treatment including chemotherapy, targeted therapy, immunotherapy, experimental agents, radiation, and surgery (except for alopecia).
• Hypersensitivity to decitabine, ASTX727, ASTX660, or any of their excipients.
• Liver cirrhosis, or chronic liver disease Child-Pugh Class B or C.
• Life-threatening illness, significant organ system dysfunction, or other condition that, in the investigator's opinion, could compromise participant safety, or the integrity of study outcomes, or interfere with the absorption or metabolism of ASTX660 or ASTX727.
• History of, or at risk for, cardiac disease.
• Known human immunodeficiency virus (HIV), active hepatitis B virus (HBV), or active hepatitis C virus (HCV) infection (participants with laboratory evidence of no active replication will be permitted).
• Known significant mental illness or other conditions, such as active alcohol or other substance abuse that, in the opinion of the investigator, predispose the participant to high risk of noncompliance with the protocol treatment or assessments.
• Treated with any investigational therapy within 2 weeks of the first dose of study treatment or treatment with a myelosuppressive therapy within 4 weeks of the first dose of study treatment.
• In Parts 1 and 2, prior treatment with decitabine for more than 2 cycles. In Part 3, any treatment with an HMA (azacitidine or decitabine, for more than one cycle).
• Inability to swallow oral medication or inability or unwillingness to comply with the administration requirements related to ASTX660-02.
  • Note: G-tube administration is not allowed.