The formation of singlet oxygen due to the energy transfer from excitons confined in silicon nanocrystals to oxygen molecules is studied using time-resolved photoluminescence spectroscopy. The process of the excitation of oxygen molecules from the ground triplet state to the second excited singlet state is studied at low temperatures, where oxygen molecules are physisorbed on the surface of silicon nanocrystals and at room temperature in gaseous oxygen ambient and in oxygen-saturated water. The low temperature measurements reveal that the energy transfer time is the shortest for the resonant energy transfer. The involvement of one energy-conserving transversal optical phonon results in about 40% increase of the energy transfer time. The excitation rate of oxygen dimers is found to be similar to that measured for oxygen molecules. At room temperature, the time of the energy transfer to oxygen molecules is about 17 mu s. The photosensitizing efficiency of silicon nanocrystals at room temperature is found to be as high as 80% for gaseous oxygen ambient and for oxygen-saturated water.