ABSTRACT Advances in instrumentation have recently extended detailed measurements of gas kinematics to large samples of high-redshift galaxies. Relative to most nearby, thin disc galaxies, in which gas rotation accurately traces the gravitational potential, the interstellar medium (ISM) of $z$ ≳ 1 galaxies is typically more dynamic and exhibits elevated turbulence. If not properly modelled, these effects can strongly bias dynamical mass measurements. We use high-resolution FIRE-2 cosmological zoom-in simulations to analyse the physical effects that must be considered to correctly infer dynamical masses from gas kinematics. Our analysis covers a range of galaxy properties from low-redshift Milky-Way-mass galaxies to massive high-redshift galaxies (M⋆ > 1011 M⊙ at $z$ = 1). Selecting only snapshots where a disc is present, we calculate the rotational profile $\bar{v}_\phi (r)$ of the cool ($10^{3.5}\,\lt {\it T}\lt 10^{4.5}~\rm {K}$) gas and compare it to the circular velocity $v_{\rm c}=\sqrt{GM_{\rm enc}/r}$. In the simulated galaxies, the gas rotation traces the circular velocity at intermediate radii, but the two quantities diverge significantly in the centre and in the outer disc. Our simulations appear to over-predict observed rotational velocities in the centres of massive galaxies (likely from a lack of black hole feedback), so we focus on larger radii. Gradients in the turbulent pressure at these radii can provide additional radial support and bias dynamical mass measurements low by up to 40 per cent. In both the interior and exterior, the gas’ motion can be significantly non-circular due to e.g. bars, satellites, and inflows/outflows. We discuss the accuracy of commonly used analytic models for pressure gradients (or ‘asymmetric drift’) in the ISM of high-redshift galaxies.