Near-field intensity statistics in semicontinuous silver films over a wide range of surface coverage are investigated using near-field scanning optical microscopy. The variance of intensity fluctuations and the high-order moments of intensity enhancement exhibit local minima at the percolation threshold. This reduction in local field fluctuations results from resonant excitation of delocalized surface plasmon modes. By probing the modification of the critical indices for high-order moments of intensity enhancement caused by the delocalized states, we provide the first experimental evidence for the coexistence of localized and delocalized surface plasmon modes in percolating metal films.