We demonstrate theoretically that laser-induced coherent quantum interference control of asymptotic states of dissociating molecules is possible even in the (one-photon) weak-field limit starting from a single vibrational eigenstate. Thus, phase dependence in the interaction with a fixed energy phase-modulated pulse can persist for some time after the pulse is over. This is illustrated for the nonadiabatic process: I+Br*←IBr→I+Br, where the relative yield of excited Br* can be changed by pure phase modulation. It is shown that the phase is able to influence wave-packet spreading in the continuum as well as the average internuclear distance in each channel. © 2014 American Physical Society.