The influence of entanglement density on the constraint renewal time is studied experimentally in transitory nonequilibrium polymer melts. The entanglement density, as quantified by the rubber elasticity, increases as the linear polymer melt transforms into the equilibrium state. The relaxation modulus obtained from linear step-strain deformations, performed at different points during the equilibration, shows an increase in constraint renewal time as the entanglement density increases. The normalized relaxation modulus curves collapse onto a single curve by rescaling the time axis with a factor G ′ ¯ (t) 0.9 (where G ′ ¯ (t) is the normalized instantaneous modulus). These findings suggest that, though the relaxation time increases with the increasing number of entanglements, the mechanism responsible for stress relaxation, after application of step-strain, is similar to that in a fully entangled melt.