Using the 2MASS second incremental data release and the zodiacal subtracted mission average maps of COBE/DIRBE, we estimate the cosmic background in the J (1.25 mum) and K (2.2 mum) bands using selected areas representing similar to 550 deg(2) of sky. We find a J background of 22.9 +/-7.0 kJy sr(-1) (54.0 +/- 16.8 nW m(-2) sr(-1)) and a K background of 20.4 +/-4.9 kJy sr(-1) (27.8 +/-6.7 nW m(-2) sr(-1)). This large-scale study shows that the main uncertainty comes from the residual zodiacal emission. The cosmic background we obtain is significantly higher than integrated galaxy counts (3.6 +/-0.8 kJy sr(-1) and 5.3 +/-1.2 kJy sr(-1) for J and K, respectively), suggesting either an increase of the galaxy luminosity function for magnitudes fainter than 30 mag or the existence of another contribution to the cosmic background from primeval stars, black holes, or relic particle decay.