Key Inclusion Criteria:

   - Meets the criteria below for the appropriate cohort:

      1. Relapsed/Refractory Cohorts: Pathologically confirmed relapsed or refractory
      (primary refractory and/or relapsed refractory) AML or confirmed intermediate,
      high, or very high risk MDS that is relapsed, refractory or intolerant to
      conventional therapy

      2. Treatment-naive/ Unfit Cohorts: Previously untreated individuals with
      histological confirmation of AML who are ineligible for treatment with a standard
      cytarabine and anthracycline induction regimen; or previously untreated
      individuals with intermediate, high, or very high risk MDS. Prior and concurrent
      therapy with hydroxyurea, oral etoposide, erythroid and/or myeloid growth factors
      is allowed.

      3. Rollover Cohort: Individuals on active magrolimab therapy on the Phase 1 AML
      (SCI-CD47-002; NCT02678338) trial who are deriving clinical benefit by
      Investigator assessment

      4. RBC transfusion dependent low risk MDS cohort: Transfusion-dependent MDS
      individuals who are very low or low risk by IPSS-R with previous treatment with
      an erythroid stimulating agent or lenalidomide.

   - White blood cell (WBC) count ≤ 20 x 10^3/mcL

   - Adequate performance status and hematological, liver, and kidney function

Key Exclusion Criteria:

   - Prior treatment with CD47 or signal regulatory protein alpha (SIRPα) targeting agents
   (with exception of magrolimab for individuals in the Rollover cohort).

   - Treatment-naive/Unfit Cohorts Only: Any prior anti-leukemic therapy (excluding
   hydroxyurea or oral etoposide), prior treatment with hypomethylating agents and/or low
   dose cytarabine.

   - Acute promyelocytic leukemia.

   - Known inherited or acquired bleeding disorders.

   - Previous allogeneic hematopoietic stem cell transplant within 6 months prior to
   enrollment, active graft versus host disease (GVHD), or requiring transplant-related
   immunosuppression.

   - Clinical suspicion of active central nervous system (CNS) involvement by leukemia

   - Known active or chronic hepatitis B or C infection or HIV

   - Pregnancy or active breastfeeding

Note: Other protocol defined Inclusion/Exclusion criteria may apply.