Context. High-mass stars and star clusters commonly form within hub-filament systems. Monoceros R2 (hereafter Mon R2), at a distance of 830 pc, harbors one of the closest of these systems, making it an excellent target for case studies. Aims. We investigate the morphology, stability and dynamical properties of the Mon R2 hub-filament system. Methods. We employed observations of the ¹³CO and C¹⁸O 1 →0 and 2 →1 lines obtained with the IRAM-30 m telescope. We also used H₂ column density maps derived from Herschel dust emission observations. Results. We identified the filamentary network in Mon R2 with the DisPerSE algorithm and characterized the individual filaments as either main (converging into the hub) or secondary (converging to a main filament). The main filaments have line masses of 30–100 M_⊙ pc⁻¹ and show signs of fragmentation, while the secondary filaments have line masses of 12–60 M_⊙ pc⁻¹ and show fragmentation only sporadically. In the context of Ostriker’s hydrostatic filament model, the main filaments are thermally supercritical. If non-thermal motions are included, most of them are transcritical. Most of the secondary filaments are roughly transcritical regardless of whether non-thermal motions are included or not. From the morphology and kinematics of the main filaments, we estimate a mass accretion rate of 10⁻⁴–10⁻³ M_⊙ yr⁻¹ into the central hub. The secondary filaments accrete into the main filaments at a rate of 0.1–0.4 × 10⁻⁴ M_⊙ yr⁻¹. The main filaments extend into the central hub. Their velocity gradients increase toward the hub, suggesting acceleration of the gas. We estimate that with the observed infall velocity, the mass-doubling time of the hub is ~2.5 Myr, ten times longer than the free-fall time, suggesting a dynamically old region. These timescales are comparable with the chemical age of the HII region. Inside the hub, the main filaments show a ring- or a spiral-like morphology that exhibits rotation and infall motions. One possible explanation for the morphology is that gas is falling into the central cluster following a spiral-like pattern.