The present invention relates to therapeutic immunoconjugates comprising SN-38 attached to an anti-HLA-DR antibody or antigen-binding antibody fragment. The immunoconjugate may be administered at a dosage of between 3 mg/kg and 18 mg/kg, preferably 4, 6, 8, 9, 10, 12, 16 or 18 mg/kg, more preferably 8, 10 or 12 mg/kg. When administered at specified dosages and schedules, the immunoconjugate can reduce solid tumors in size, reduce or eliminate metastases and is effective to treat cancers resistant to standard therapies, such as radiation therapy, chemotherapy or immunotherapy. The methods and compositions are particularly useful for treating AML, ALL or multiple myeloma.