The concept of the Lorentz-invariant mass of groups of photons is shown to be applicable to classical light pulses with finite sizes and duration. Diffraction of light, providing non-collinearity of the photon motion in pulses, provides also nonzero values of their Lorentz-invariant masses. By considering light pulses as relativistic objects we find that owing to diffraction and finiteness of the Lorentz-invariant mass the mean propagation speed of pulses is always smaller than the light speed c.