Context. The Sun has recently been predicted to be an extended source of gamma-ray emission, produced by inverse-Compton (IC) scattering of cosmic-ray (CR) electrons on the solar radiation field. The emission was predicted to be extended and a confusing foreground for the diffuse extragalactic background even at large angular distances from the Sun. The solar disk is also expected to be a steady gamma-ray source. While these emissions are expected to be readily detectable in the future by GLAST, the situation for available EGRET data is more challenging. Aims. The theory of gamma-ray emission from IC scattering on the solar radiation field by Galactic CR electrons is given in detail. This is used as the basis for detection and model verification using EGRET data. Methods. We present a detailed study of the solar emission using the EGRET database, accounting for the effect of the emission from 3C 279, the moon, and other sources, which interfere with the solar emission. The analysis was performed for 2 energy ranges, above 300 MeV and for 100-300 MeV, as well as for the combination to improve the detection statistics. The technique was tested on the moon signal, with our results consistent with previous work. Results. Analyzing the EGRET database, we find evidence of emission from the solar disk and its halo. The observations are compared with our model for the extended emission. The spectrum of the solar disk emission and the spectrum of the extended emission have been obtained. The spectrum of the moon is also given. Conclusions. The observed intensity distribution and the flux are consistent with the predicted model of IC gamma-rays from the halo around the Sun.
