Sun induced chlorophyll fluorescence (SICF) emitted by phytoplankton provides considerable insights into the vital role of the carbon productivity of the earth's aquatic ecosystems. However, the SICF signal leaving a water body is highly affected by the high spectral variability of its optically active constituents. To disentangle the SICF emission from the water-leaving radiance, a new high spectral resolution retrieval algorithm is presented, which significantly improves the fluorescence line height (FLH) method commonly used so far. The proposed algorithm retrieves the reflectance without SICF contribution by the extrapolation of the reflectance from the adjacent regions. Then, the SICF emission curve is obtained as the difference of the reflectance with SICF, the one actually obtained by any remote sensor (apparent reflectance), and the reflectance without SICF, the one estimated by the algorithm (true reflectance). The algorithm first normalizes the reflectance spectrum at 780 nm, following the similarity index approximation, to minimize the variability due to other optically active constituents different from chlorophyll. Then, the true reflectance is estimated empirically from the normalized reflectance at three wavelengths using a machine learning regression algorithm (MLRA) and a cubic spline fitting adjustment. Two large reflectance databases, representing a wide range of coastal and ocean water components and scattering conditions, were independently simulated with the radiative transfer model HydroLight and used for training and validation of the MLRA fitting strategy. The best results for the high spectral resolution SICF retrieval were obtained using support vector regression, with relative errors lower than 2% for the SICF peak value in 81% of the samples. This represents a significant improvement with respect to the classic FLH algorithm, applied for OLCI bands, for which the relative errors were higher than 40% in 59% of the samples.