Temporal Bragg diffraction-induced laser pulse splitting (DIPS) into two ones propagating with different group velocities is observed in multilayered linear photonic crystals (PC). This phenomenon originates from spatially inhomogeneous light localization within the PC at the Laue scheme of the dynamical Bragg diffraction. In a homogenous medium at the PC output each pulse is spatially separated into two pulses, propagating in the transmission and diffraction directions, respectively. The experiments are carried out for one-dimensional porous silicon-based PC consisting of 375 spatial periods of 800 nm thick and using a femtosecond Ti-sapphire laser as a probe. A linear dependence of the time splitting of each pair of transmitted and diffractively reflected pulses on the crystal thickness is demonstrated and is supported by theoretical estimations.