We present new maps of emission-line flux distributions and kinematics in both ionized (traced by HI and [FeII] lines) and molecular (H2) gas of the inner 0.7x0.7kpc2 of the galaxy NGC4303, with a spatial resolution 40-80pc and velocity resolution 90-150 km/s obtained from near-IR integral field specroscopy using the VLT instrument SINFONI. The most promiment feature is a 200-250pc ring of circum-nuclear star-forming regions. The emission from ionized and molecular gas shows distinct flux distributions: while the strongest HI and [FeII] emission comes from regions in the west side of the ring (ages~4Myr), the H2 emission is strongest at the nucleus and in the east side of the ring (ages>10Myr). We find that regions of enhanced hot H2 emission are anti-correlated with those of enhanced [FeII] and HI emission, which can be attributed to post starburst regions that do not have ionizing photons anymore but still are hot enough (~2000K) to excite the H2 molecule. The line ratios are consistent with the presence of an AGN at the nucleus. The youngest regions have stellar masses in the range 0.3-1.5E5 MSun and ionized and hot molecular gas masses of ~0.25-1.2E4 Msun and 2.5-5 Msun, respectively. The stellar and gas velocity fields show a rotation pattern, with the gas presenting larger velocity amplitudes than the stars, with a deviation observed for the H2 along the nuclear bar, where increased velocity dispersion is also observed, possibly associated with non circular motions along the bar. The stars in the ring show smaller velocity dispersion than the surroundings, that can be attributed to a cooler dynamics due to their recent formation from cool gas.