Catalyzes the synthesis of activated sulfate. adenosine 5'-phosphosulfate + ATP = 3'-phosphoadenylyl sulfate + ADP + H(+) Sulfur metabolism; hydrogen sulfide biosynthesis; sulfite from sulfate: step 2/3. Up-regulated by sulfur starvation and repressed by cysteine. Also induced by O-acetyl-L-serine (OAS), a direct precursor of cysteine, maybe via inactivation of a putative transcriptional repressor of the cysH operon whose activity is controlled by the intracellular levels of OAS. Belongs to the APS kinase family.