The estimation of tritium inventories and permeation fluxes to the coolant in the International Thermonuclear Experimental Reactor (ITER) is an important issue from the safety standpoint. Previous calculations have been performed neglecting ITER's pulse operation because it was assumed that during plasma-off periods the processes become "frozen" until the plasma starts again. It is shown that this assumption may fail in certain cases, particularly in the first wall of ITER, where a larger (by an order of magnitude) inventory and permeation flux to the coolant is obtained when pulse operation is considered. The calculations are performed with the code TMAP4. The discontinuous nature of the plasma operation is mimicked by imposing on the plasma-facing side a heat flux and a particle implantation flux in the form of a quadratic stepwise periodic function oscillating between zero (plasma off) and a maximum value (plasma on).