Context. The formation and evolution of planetary systems impact the evolution of the primordial accretion disk in its dust and gas content. HD 141569 is a peculiar object in this context as it is the only known pre-main sequence star characterized by a hybrid disk. Observations with 8 m class telescopes probed the outer-disk structure showing a complex system of multiple rings and outer spirals. Furthermore, interferometric observations attempted to characterize its inner 5 au region, but derived limited constraints. Aims. The goal of this work was to explore with new high-resolution interferometric observations the geometry, properties, and dynamics of the dust and gas in the internal regions of HD 141569. Methods. We observed HD 141569 on milliarcsecond scales with GRAVITY/VLTI in the near-infrared (IR) at low (R ∼20) and high (R ∼4000) spectral resolution. We interpreted the interferometric visibilities and spectral energy distribution with geometrical models and through radiative transfer techniques using the code MCMax to constrain the dust emission. We analyzed the high spectral resolution quantities (visibilities and differential phases) to investigate the properties of the Brackett-γ (Brγ) line emitting region. Results. Thanks to the combination of three different epochs, GRAVITY resolves the inner dusty disk in the K band with squared visibilities down to V2 ∼ 0.8. A differential phase signal is also detected in the region of the Brγ line along most of the six baselines. Data modeling shows that an IR excess of about 6% is spatially resolved and that the origin of this emission is confined in a ring of material located at a radius of ∼1 au from the star with a width . 0.3 au. The MCMax modeling suggests that this emission could originate from a small amount (1.4 × 10−8 M⊕) of quantum-heated particles, while large silicate grain models cannot reproduce at the same time the observational constraints on the properties of near-IR and mid-IR fluxes. The high spectral resolution differential phases in the Brγ line clearly show an S-shape that can be best reproduced with a gaseous disk in Keplerian rotation, confined within 0.09 au (or 12.9 R?). This is also hinted at by the double-peaked Brγ emission line shape, known from previous observations and confirmed by GRAVITY. The modeling of the continuum and gas emission shows that the inclination and position angle of these two components are consistent with a system showing relatively coplanar rings on all scales. Conclusions. With a new and unique observational dataset on HD 141569, we show that the complex disk of this source is composed of a multitude of rings on all scales. This aspect makes HD 141569 a potentially unique source to investigate planet formation and disk evolution in intermediate-mass pre-main sequence stars.