We report on a sensitive search for H₂ 1-0 S(1), 1-0 S(0) and 2-1 S(1) ro-vibrational emission at 2.12, 2.22 and 2.25 μm in a sample of 15 Herbig Ae/Be stars employing CRIRES, the ESO-VLT near-infrared high-resolution spectrograph, at R ~ 90 000. We report the detection of the H₂ 1-0 S(1) line toward HD 100546 and HD 97048. In the other 13 targets, the line is not detected. The H₂ 1-0 S(0) and 2-1 S(1) lines are undetected in all sources. These observations are the first detection of near-IR H₂ emission in HD 100546. The H₂ 1-0 S(1) lines observed in HD 100546 and HD 97048 are observed at a velocity consistent with the rest velocity of both stars, suggesting that they are produced in the circumstellar disk. In HD 97048 the emission is spatially resolved and it is observed to extend at least up to 200 AU from the star. We report an increase of one order of magnitude in the H₂ 1-0 S(1) line flux with respect to previous measurements taken in 2003 for this star, which suggests line variability. In HD 100546 the emission is tentatively spatially resolved and may extend at least up to 50 AU from the star. Modeling of the H₂ 1-0 S(1) line profiles and their spatial extent with flat Keplerian disks shows that most of the emission is produced at a radius larger than 5 AU. Upper limits to the H₂ 1-0 S(0)/1-0 S(1) and H₂ 2-1 S(1)/1-0 S(1) line ratios in HD 97048 are consistent with H₂ gas at T > 2000 K and suggest that the emission observed may be produced by X-ray excitation. The upper limits for the line ratios for HD 100546 are inconclusive. Because the H₂ emission is located at large radii, for both sources a thermal emission scenario (i.e., gas heated by collisions with dust) is implausible. We argue that the observation of H₂ emission at large radii may be indicative of an extended disk atmosphere at radii >5 AU. This may be explained by a hydrostatic disk in which gas and dust are thermally decoupled or by a disk wind caused by photoevaporation.