A search is presented for long-lived particles decaying into an oppositely charged lepton pair, μ⁺, μ⁻, or e^±μ^∓, that form a vertex within the inner tracking system of the ATLAS detector at the Large Hadron Collider, displaced from the primary proton–proton interaction region. The analysis uses the 140 fb⁻¹ of Run-2 data collected at √𝑠 = 13 TeV by the ATLAS experiment in 2015–2018. The results of the analysis are interpreted in the context of three benchmark models covering masses from 0.1 to 2.2 TeV and a range of mean proper lifetimes times the speed of light from 1 to 10 000 mm. The first model is a generic Z′ boson pair-produced by a new heavy scalar, with the Z′ decaying into lepton pairs. The remaining two models are R-parity violating supersymmetric models in which the lightest neutralino decays into 𝓁+𝓁′−𝜈 (𝓁, 𝓁′= e, μ). The models differ by the mode of production of the , which can be produced via the decay of pairs of gluinos or of pairs of charginos and neutralinos (, , or ). Although each benchmark sample includes pair-produced LLPs, only a single vertex is required to be reconstructed. No dilepton displaced vertex candidate is observed and the results are presented as upper limits on the production cross-sections. This analysis sets leading limits on the production cross-sections for multiple models, including parameter space that has never been directly probed.