We study the effect of solidification kinetics, driven by local limited diffusion in the liquid, on macrosegregation. If the diffusion in the liquid surrounding a growing grain is slow, the local average liquid concentration is lower than the thermodynamic equilibrium concentration at the interface. The redistribution of solute by the flow of intergranular liquid on the macroscopic scale is affected by the modified microsegregation in the liquid. We study this phenomenon using a two-phase model based on the volume-averaging method, describing macroscopic transport coupled to a microscopic grain growth model. The growth kinetics is resolved by accounting for finite diffusion in the liquid and solid phases, assuming an equiaxed globular morphology. To accurately model the diffusion field around the grain, we propose an improved approximation for the solutal boundary layer thickness accounting for the growth conditions and liquid convection. The effect of growth kinetics on macrosegregation is then investigated in the case of solidification of a binary alloy in a small cavity where the solid phase is fixed and fluid flow is driven by natural convection. We show that it is important to accurately model the diffusion field around the grain to correctly capture the effect of growth kinetics on the weakening of macrosegregation.