During its three flybys of Mercury, the MESSENGER spacecraft made the first detection of gamma-ray emission from the planet's surface. With a closest approach distance of ̃200 km, the flybys provided an opportunity to measure elemental abundances of Mercury's near-equatorial regions, which will not be visited at low altitude during MESSENGER's orbital mission phase. Despite being limited by low planetary photon flux, sufficient counts were accumulated during the first two flybys to estimate bounds on abundances for some elements having relatively strong gamma-ray spectral peaks, including Si, Fe, Ti, K, and Th. Only for Si is the standard deviation σ sufficiently small to conclude that this element was detected with 99% confidence. Iron and potassium are detected at the 2- σ (95% confidence) level, whereas only upper bounds on Ti and Th can be determined. Relative to a Si abundance assumed to be 18 weight percent (wt%), 2- σ upper bounds have been estimated as 9.7 wt% for Fe, 7.0 wt% for Ti, 0.087 wt% for K, and 2.2 ppm for Th. The relatively low upper bound on K rules out some previously suggested models for surface composition for the regions sampled. Upper bounds on Fe/Si and Ti/Si ratios are generally consistent with Ti and Fe abundances estimated from the analysis of measurements by the MESSENGER Neutron Spectrometer during the flybys but are also permissive of much lower concentrations.