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). {ECO:0000250|UniProtKB:Q80ZG2, ECO:0000269|PubMed:11085927, ECO:0000269|PubMed:12747803}. This is the function of ITPKC (inositol-trisphosphate 3-kinase C, ENSG00000086544).