Catalyzes the phosphorylation of 1D-myo-inositol 1,4,5-trisphosphate (InsP3) into 1D-myo-inositol 1,3,4,5-tetrakisphosphate and participates to the regulation of calcium homeostasis (PubMed:11085927, PubMed:12747803). Can phosphorylate inositol 2,4,5-triphosphate to inositol 2,4,5,6-tetraphosphate (By similarity).