Halide perovskites are promising semiconductor materials for optoelectronics. One of their unique features is the synthesis, that could be performed by the crystallization from the solution. This method is fast, but practically couldn't be optimized due to the strongly non-equilibrium conditions of crystal growth. Another quality limitation is the typical incorporation of organic solvent molecules into crystals when perovskite crystallization is performed from solution with organic solvent. Here we report an alternative method of perovskite single crystal growth based on the counterdiffusion of reagents in the gel medium. This counterdiffusion-in-gel crystallization (CGC) method is based on the difference of solubility between perovskites and lead halide in the corresponding halide acid, HX. The difference of solubility between perovskites and lead halide leads to the formation of perovskite single crystals of sufficiently large size with an excellent optical quality at constant room temperature. Particularly, here we report the growth of MAPbI₃ and MAPbBr₃ halide perovskite single crystals (MA = CH₃NH₃⁺) by the counterdiffusion of the organic-solvent-free reagents in the U-tube filled with the silica gel. Their photoluminescence spectra recorded at 4 K demonstrate the excitonic resonances with the full width <2.5 meV, which proves their excellent optical quality. The proposed method can be used in fabrication of high-quality halide perovskite single crystals for both fundamental research, and for applications where the absence of defects is a critical requirement.