The observation of superconductivity in La₃Ni₂O_7–δ under pressure, following the suppression of a high-temperature density wave state, has attracted considerable attention. The nature of this density wave order was not clearly identified. Here we probe the magnetic response of the zero-pressure phase of La₃Ni₂O_7–δ as hydrostatic pressure is applied, and find that the apparent single density wave transition at zero applied pressure splits into two. The comparison of our muon-spin rotation and relaxation experiments with dipole-field numerical analysis reveals the magnetic structure’s compatibility with a stripe-type arrangement of Ni moments, characterized by alternating lines of magnetic moments and non-magnetic stripes at ambient pressure. When pressure is applied, the magnetic ordering temperature increases, whereas the unidentified density wave transition temperature falls. Our findings reveal that the ground state of the La₃Ni₂O_7–δ system is characterized by the coexistence of two distinct orders—a magnetically ordered spin density wave and a lower-temperature ordering that is most probably a charge density wave—with a notable pressure-enhanced separation between them.