Catalyzes cross-linking of the peptidoglycan cell wall at the division septum. Preferential cleavage: (Ac)2-L-Lys-D-Ala-|-D-Ala. Also transpeptidation of peptidyl-alanyl moieties that are N-acyl substituents of D-alanine. Cell wall biogenesis; peptidoglycan biosynthesis. Interacts with FtsN and FtsW. Localization varies during the cell cycle. At the beginning of the cell cycle, it accumulates at the new cell pole. Later during the cell cycle, polar accumulation disappears concomitantly with the re-localization to the FtsZ ring in a FtsZ-dependent manner. A portion of FtsI molecules is also diffusely dispersed around the membrane during both cell elongation and division. The active site is important for FtsI localization. Belongs to the transpeptidase family.