We present the experimental demonstration of what are to our knowledge the first two-dimensional planar plasmonic lenses formed by an array of spatially varying cross-shaped apertures in a metallic film for Fresnel-region focusing. The design utilizes localized surface plasmon resonances occurring inside the apertures, accompanied by an aperture geometry dependent phase shift, to achieve the desired spatial phase modulation in the transmitted field. The performance of lenses with different design configurations was evaluated using a confocal scanning optical microscope, and the effects of diffraction on the optical response of these microscale devices are discussed.