We have investigated the dynamics of water confined in a molecular sieve, with a cylindrical pore diameter of 10 A, by means of quasielastic neutron scattering (QENS). Both the incoherent and coherent intermediate scattering functions I(Q,t) were determined by time-of-flight QENS and the neutron spin-echo technique, respectively. The results show that I(Q,t) is considerably more stretched in time with a slightly larger average relaxation time in the case of coherent scattering. From the Q dependence of I(Q,t) it is clear that the observed dynamics is almost of an ordinary translational nature. A comparison with previous dielectric measurements suggests a possible merging of the alpha and beta relaxations of the confined water at T=185 K, although the alpha relaxation cannot be directly observed at lower temperatures due to the severe confinement. The present results are discussed in relation to previous results for water confined in a Na-vermiculite clay, where the average relaxation time from spin-echo measurements was found to be slower than in the present system (particularly at low temperatures).