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In underdoped cuprates, a putative pair density wave (PDW) state has been suggested to be responsible for the pseudogap regime, but the evidence for a PDW remains inconclusive. To test the interlayer frustration, the crucial component of the PDW picture, we performed transport measurements on La_1.7Eu_0.2Sr_0.1CuO₄ and La_1.48Nd_0.4Sr_0.12CuO₄ with “striped” spin and charge orders in perpendicular magnetic fields H_perp, and we also applied an additional field parallel to CuO₂ layers (H_para). We detected several phenomena predicted to arise from the existence of a PDW, including an enhancement of interlayer superconducting (SC) phase coherence with increasing H_para. Our results are consistent with the presence of local, PDW pairing correlations that compete with the uniform SC order at temperatures T_c⁰ < T < (2-6)T_c⁰, where T_c⁰ is the zero-field SC transition temperature, and become dominant at high enough H_perp as T→0.