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Context. Ionized interstellar gas is an important component of the interstellar medium and its lifecycle. The recent evidence for a widely distributed highly ionized warm interstellar gas with a density intermediate between the warm ionized medium (WIM) and compact H  II regions suggests that there is a major gap in our understanding of the interstellar gas. Aims. Our goal is to investigate the properties of the dense WIM in the Milky Way using spectrally resolved SOFIA GREAT [N  II ] 205 μm fine-structure lines and Green Bank Telescope hydrogen radio recombination lines (RRL) data, supplemented by spectrally unresolved Herschel PACS [N  II ] 122μm data, and spectrally resolved 12 CO. Methods. We observed eight lines of sight (LOS) in the 20° < l < 30° region in the Galactic plane. We analyzed spectrally resolved lines of [N  II ] at 205 μm and RRL observations, along with the spectrally unresolved Herschel PACS 122 μm emission, using excitation and radiative transfer models to determine the physical parameters of the dense WIM. We derived the kinetic temperature, as well as the thermal and turbulent velocity dispersions from the [N  II ] and RRL linewidths. Results. The regions with [N  II ] 205 μm emission are characterized by electron densities, n ( e ) ~ 10−35 cm −3 , temperatures range from 3400 to 8500 K, and nitrogen column densities N(N + ) ~ 7 × 10 16 to 3 × 10 17 cm −2 . The ionized hydrogen column densities range from 6 × 10 20 to 1.7 × 10 21 cm −2 and the fractional nitrogen ion abundance x (N + ) ~ 1.1 × 10 −4 to 3.0 × 10 −4 , implying an enhanced nitrogen abundance at a distance ~4.3 kpc from the Galactic Center. The [N  II ] 205 μm emission lines coincide with CO emission, although often with an offset in velocity, which suggests that the dense warm ionized gas is located in, or near, star-forming regions, which themselves are associated with molecular gas. Conclusions. These dense ionized regions are found to contribute ≳50% of the observed [C  II ] intensity along these LOS. The kinetic temperatures we derive are too low to explain the presence of N + resulting from electron collisional ionization and/or proton charge transfer of atomic nitrogen. Rather, these regions most likely are ionized by extreme ultraviolet (EUV) radiation from nearby star-forming regions or as a result of EUV leakage through a clumpy and porous interstellar medium.