Context. Studying the physical conditions in circumstellar disks is a crucial step toward understanding planet formation and disk evolution. Of particular interest is the case of HD 100546, a Herbig Be star that presents a gap within the first 13 AU of its protoplanetary disk, a gap that may originate in the dynamical interactions of a forming planet with its hosting disk. Aims. We seek a more detailed understanding of the structure of the circumstellar environment of HD 100546 and refine our previous disk model that is composed of a tenuous inner disk, a gap and a massive outer disk (see Benisty et al. 2010, A&A, 511, A75). We also investigate whether planetary formation processes can explain the complex density structure observed in the disk. Methods. We gathered a large amount of new interferometric data using the AMBER/VLTI instrument in the H- and K-bands to spatially resolve the warm inner disk and constrain its structure. Then, combining these measurements with photometric observations, we analyze the circumstellar environment of HD 100546 in the light of a passive disk model based on 3D Monte-Carlo radiative transfer. Finally, we use hydrodynamical simulations of gap formation by planets to predict the radial surface density profile of the disk and test the hypothesis of ongoing planet formation. Results. The SED (spectral energy distribution) from the UV to the millimeter range, and the NIR (near-infrared) interferometric data are adequately reproduced by our model. We show that the H- and K-band emissions are coming mostly from the inner edge of the internal dust disk, located near 0.24 AU from the star, i.e., at the dust sublimation radius in our model. At such a short distance, the survival of hot (silicate) dust requires the presence of micron-sized grains, heated at  ~1750 K. We directly measure an inclination of 33° ± 11° and a position angle of 140° ± 16° for the inner disk. This is similar to the values found for the outer disk (i ≃ 42°, PA ≃ 145°), suggesting that both disks may be coplanar. We finally show that 1 to 8 Jupiter mass planets located at  ~8 AU from the star would have enough time to create the gap and the required surface density jump of three orders of magnitude between the inner and outer disk. However, no information on the amount of matter left in the gap is available, which precludes us from setting precise limits on the planet mass, for now.