ITER operations require effective fuelling of the core plasma for conditions in which neutral dynamics through the scrape-off layer (SOL) is expected to affect significantly the efficiency of gas penetration. On the basis of previous analysis for stationary conditions, pellets are foreseen to provide core fuelling of high-Q DT scenarios. In this paper we present a modelling study of the gas fuelling efficiency in ITER DT reference scenarios providing an estimate of the upper plasma density achievable with gas fuelling only. Integrated core-edge plasma simulations for various phases of ITER 15 MA/5.3T DT H-mode plasmas, including the stationary H-mode conditions, the H-mode access phase and the preceding L-mode phases, have been carried out with the JINTRAC suite of codes for ITER as well as for lower plasma currents at 5.3T (10 MA, 7.5 MA and 5 MA). In addition a DT plasma scenario with plasma current of 7.5MA and toroidal field of 2.65T representative of lower field operation in ITER has also been studied. The simulations for 15 MA L-mode plasmas indicate that divertor detachment sets the maximum density achievable at the separatrix by deuterium-tritium gas fuelling. This, together with core transport, determines the maximum achievable volume-averaged plasma density, which appears to be ~ 2.5-3.0 10 19 m -3 for a range of SOL transport assumptions considered to be appropriate for these ITER conditions. This level of volume-average density is close to that required for stationary application of NBI heating at full power (16.5 MW per injector) and ion energy (1 MeV) compatible with acceptable shine-through loads on the first wall. For plasma currents of 5-10 MA the maximum achievable L-mode densities with gas puffing are lower than those at 15 MA implying the need for pellet fuelling for L-mode plasmas in ITER to achieve densities in the range of ~ 2.5-3.0 10 19 m -3 . Simulations of gas fuelled DT H-mode plasmas in ITER show that the plasma density increases rapidly after the H-mode transition due to an increased penetration of the neutrals to the core plasma during the initial phase of the H-mode, associated with low divertor power fluxes and the establishment of the edge transport barrier, but that this increase is short lived and saturates as soon as the edge power flux increases and core plasma neutral penetration decreases. The achievable density in gas fuelled H-modes is typically a factor of 2-3 larger than in L-modes for 15 MA DT plasmas in ITER because of the higher edge power flux which raises the detachment limit and the lower plasma collisionalities which increase the anomalous inwards particle pinch. The fusion performance of gas fuelled Hmodes at 15 MA is typically found to be moderately high (Q ~ 6-8) due to higher separatrix densities reached and the density in the edge transport barrier being flat (due to low core neutral source), which leads to the pedestal temperature to exceed ~ 6.5 keV and to a high fusion reaction rate throughout the plasma volume. The sensitivity of the modelling results to modelling assumptions and the need for validation of the physics assumptions in the modelling studies are discussed.