We present new ∼1 arcsec resolution data of the dense molecular gas in the central 50–100 pc of four nearby Seyfert galaxies. Plateau de Bure Interferometer (PdBI) observations of HCN and, in two of the four sources, simultaneously HCO+ allow us to carefully constrain the dynamical state of the dense gas surrounding the active galactic nuclei (AGN). The analysis of the kinematics shows large line widths of 100–200 km s−1 full width at half-maximum (FWHM) that can only partially arise from beam smearing of the velocity gradient. The observed morphological and kinematic parameters (dimensions, major axis position angle, red and blue channel separation, and integrated line width) are well reproduced by a thick disc, where the emitting dense gas has a large intrinsic dispersion (20–40 km s−1), implying that it exists at significant scale heights (25–30 per cent of the disc radius). To put the observed kinematics in the context of the starburst and AGN evolution, we estimate the Toomre Q parameter. We find this is always greater than the critical value, i.e. Q is above the limit such that the gas is stable against rapid star formation. This is supported by the lack of direct evidence, in these four Seyfert galaxies, for on-going star formation close around the AGN. Instead, any current star formation tends to be located in a circumnuclear ring. We conclude that the physical conditions are indeed not suited to star formation within the central ∼100 pc.