We have constructed an inverse estimate of surface fluxes of carbon dioxide using both atmospheric and oceanic observational constraints. This global estimate is spatially resolved into 11 land regions and 11 ocean regions, and is calculated as a temporal mean for the period 1992--1996. The method interprets in situ observations of carbon dioxide concentration in the ocean and atmosphere with transport estimates from global circulation models. Uncertainty in the modeled circulation is explicitly considered in this inversion by using a suite of 16 atmospheric and 10 oceanic transport simulations. The inversion analysis, coupled with estimates of river carbon delivery, indicates that the open ocean had a net carbon uptake from the atmosphere during the period 1992--96 of 1.7 PgC yr-1, consisting of an uptake of 2.1 PgC yr-1 of anthropogenic carbon and a natural outgassing of about 0.5 PgC yr-1 of carbon fixed on land and transported through rivers to the open ocean. The formal uncertainty on this oceanic uptake, despite a comprehensive effort to quantify sources of error due to modeling biases, uncertain riverine carbon load, and biogeochemical assumptions, is driven down to 0.2 PgC yr-1 by the large number and relatively even spatial distribution of oceanic observations used. Other sources of error, for which quantifiable estimates are not currently available, such as unresolved transport and large region inversion bias, may increase this uncertainty.