In the search for alternative chemotherapeutic strategies against leukemia, various 1-indanone thiosemicarbazones, as well as eight novel platinum(II) and palladium(II) complexes, with the formula [MCl₂(HL)] and [M(HL)(L)]Cl, derived from two 1-indanone thiosemicarbazones were synthesized and tested for antiproliferative activity against the human leukemia U937 cell line. The crystal structure of [Pt(HL1)(L1)]Cl·2MeOH, where L1=1-indanone thiosemicarbazone, was solved by X-ray diffraction. Free thiosemicarbazone ligands showed no antiproliferative effect, but the corresponding platinum(II) and palladium(II) complexes inhibited cell proliferation and induced apoptosis. Platinum(II) complexes also displayed selective apoptotic activity in U937 cells but not in peripheral blood monocytes or the human hepatocellular carcinoma HepG2 cell line used to screen for potential hepatotoxicity. Present findings show that, in U937 cells, 1-indanone thiosemicarbazones coordinated to palladium(II) were more cytotoxic than those complexed with platinum(II), although the latter were found to be more selective for leukemic cells suggesting that they are promising compounds with potential therapeutic application against hematological malignancies.