Analyzing the kinematics of filamentary molecular clouds is a crucial step toward understanding their role in the star formation process. Therefore, we study the kinematics of 283 filament candidates in the inner Galaxy, that were previously identified in the ATLASGAL dust continuum data. The ¹³CO(2 – 1) and C¹⁸O(2 – 1) data of the SEDIGISM survey (Structure, Excitation, and Dynamics of the Inner Galactic Inter Stellar Medium) allows us to analyze the kinematics of these targets and to determine their physical properties at a resolution of 30′′ and 0.25 km s⁻¹. To do so, we developed an automated algorithm to identify all velocity components along the line-of-sight correlated with the ATLASGAL dust emission, and derive size, mass, and kinematic properties for all velocity components. We find two-third of the filament candidates are coherent structures in position-position-velocity space. The remaining candidates appear to be the result of a superposition of two or three filamentary structures along the line-of-sight. At the resolution of the data, on average the filaments are in agreement with Plummer-like radial density profiles with a power-law exponent of p ≈ 1.5 ± 0.5, indicating that they are typically embedded in a molecular cloud and do not have a well-defined outer radius. Also, we find a correlation between the observed mass per unit length and the velocity dispersion of the filament of m ∝ σ_v². We show that this relation can be explained by a virial balance between self-gravity and pressure. Another possible explanation could be radial collapse of the filament, where we can exclude infall motions close to the free-fall velocity.