A total of six deep exposures (using the astronomical observation template CAM01 with a 6" pixel field of view) through the ISOCAM LW10 filter (IRAS band 1, i.e., 12 μm) were obtained on a ~15' square field centered on the ecliptic plane. Point sources were extracted using the technique described in 1999 by Désert et al. Two known asteroids appear in these frames, and 20 sources moving with velocities appropriate for main-belt asteroids are present. Most of the asteroids detected have flux densities less than 1 mJy, that is, between 150 and 350 times fainter than any of the asteroids observed by IRAS. These data provide the first direct measurement of the 12 μm sky-plane density for asteroids on the ecliptic equator. The median zodiacal foreground, as measured by ISOCAM during this survey, is found to be 22.1+/-1.5 mJy pixel-1, i.e., 26.2+/-1.7 MJy sr-1. The results presented here imply that the actual number of kilometer-sized asteroids may be higher than several recent estimates based upon observations at visual wavelengths and are in reasonable agreement with the statistical asteroid model. Using results from the observations presented here, together with three other recent population estimates, we conclude that the cumulative number of main-belt asteroids with diameters greater than 1 km is (1.2+/-0.5)×106. Based on observations with the Infrared Space Observatory (ISO), an ESA project with instruments funded by ESA Member states (especially the PI countries: France, Germany, the Netherlands, and the UK) with the participation of ISAS and NASA.