We examine the basic acceleration mechanisms acting on the ionized gas in the narow line region (NLR) of Seyfert galaxies. Specifically, are the [O III] lambda-5007 line widths determined by "active" processes unique to AGNs, or "passive" processes such as motion in the gravitational potential of the host galaxy? A sample of 140 Seyfert galaxies is analyzed using parameters which track nuclear perturbation (e.g., radio morphology and luminosity) and host virial velocity (e.g., observed and inclination corrected rotation amplitude, DELTA-V(rot) and DELTA-V(rot)c). A plot of [O III] FWHM versus rotation amplitude, DELTA-V(rot), reveals the importance of both virial and nonvirial motion. For Seyferts without linear radio sources, a very strong correlation is found with a best-fit relation FWHM congruent-to DELTA-V(rot) (R approximately 0.6, P(null) approximately 10(-5). Clearly, gravity plays a key role in the NLR. However, a relatively well defined group of Seyferts with linear radio morphology and high radio luminosity (L1415 greater-than-or-equal-to 10(22.5) W Hz-1) have significantly broader [O III] lines, suggesting an additional acceleration mechanism is present. Long-slit observations of these objects often reveal high-velocity components approximately coincident with the near-nuclear radio lobes. It seems that the jet which powers the radio source also accelerates ionized gas, creating a super-virial bipolar flow. If the high-velocity jet-perturbed contributions are deblended, the residual profiles rejoin the rest of the sample close to the virial relation. The origin of the [O III] FWHM versus DELTA-V(rot) relation is intriguing since these parameters are defined on very different length scales. The possibility that a normal spiral rotation curve can be fully smeared across a nuclear aperture is explored using the data of Rubin and collaborators. It seems that nuclear gas velocity gradients in normal spirals are too shallow to explain the FWHM versus DELTA-V(rot) correlation in Seyfert galaxies, although a 50% rotational contribution to the FWHM may be common, increasing to approximately 100% for more distant objects. On the other hand, if rotational smearing is important, then Seyfert galaxies may have unusually steep nuclear rotation curves and/or isolated rapidly rotating cores. Faster nuclear gas rotation in Seyferts may either signify higher nuclear mass density, or full centrifugal support within the bulge. An alternative possibility is that NLR motion resembles stellar dispersion, and that DELTA-V(rot) indirectly represents V(sigma), the nuclear stellar velocity dispersion. Using a large sample of normal spirals, the relation between DELTA-V(rot)c and V(sigma) is defined and used to estimate V(sigma) for the Seyferts. There is a good correlation between [O III] FWHM and these estimated stellar dispersions (R approximately 0.6, P(null) approximately 10(-5)), with best-fit yielding FWHM[O III] congruent-to 0.9 x FWHM(stars)est, consistent with dispersion support in the NLR. Three separate tests are used to establish the degree to which [O III] FWHM reflects virial motion confined to the galactic plane (e.g., disk rotation) or virial motion independent of it (e.g., dispersion or tilted rotation). All three tests suggest that the NLR velocities are neither fully confined to the plane nor fully independent of it, but that both components are present. Paper III extends the analysis by considering galaxy and spheroidal luminosity as alternative virial parameters.
