The lowest (main) and high-order Mie resonances and the Bragg-like multiple scattering of electromagnetic (EM) waves are determined as three mechanisms of formation and frequency position of two opaque bands, with narrow peaks in one of the bands in the transmission spectra of 2D photonic crystals composed of dielectric cylinders arranged parallel to the EM wave's electric vector in the square lattice. The main Mie resonance in a single cylinder defines the frequency position of the main gap whose formation results from the Bragg-like scattering. An additional gap with narrow transmission peaks opens in the spectrum of a cylinder layer and becomes pronounced with the number of layers. It is argued that higher-order Mie resonances are responsible for the transmission peaks within the additional band of a perfect crystal. It is shown that 2D photonic crystals with a filling factor ranging from 3% to 20% at a fixed crystal period may be a good zero approximation to study wave transmission through a localizing 2D dense random medium slab.
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