High-pressure neutron powder diffraction, muon-spin rotation, and magnetization studies of the structural, magnetic, and the superconducting properties of the Ce-underdoped superconducting (SC) electron-doped cuprate system with the Nd₂CuO₄ (the so-called T′) structure T′−Pr_1.3−xLa_0.7Ce_xCuO₄ with x=0.1 are reported. A strong reduction of the in-plane and out-of-plane lattice constants is observed under pressure. However, no indication of any pressure-induced phase transition from T′ to the K₂NiF₄ (the so-called T) structure is observed up to the maximum applied pressure of p = 11 GPa. Large and nonlinear increase of the short-range magnetic order temperature T_so in T′−Pr_1.3−xLa_0.7Ce_xCuO₄ (x=0.1) was observed under pressure. Simultaneous pressure causes a nonlinear decrease of the SC transition temperature T_c. All these experiments establish the short-range magnetic order as an intrinsic and competing phase in SC T′−Pr_1.3-xLa_0.7Ce_xCuO₄ (x=0.1). The observed pressure effects may be interpreted in terms of the improved nesting conditions through the reduction of the in-plane and out-of-plane lattice constants upon hydrostatic pressure.