We present results of two observing campaigns conducted by the OGLE-III survey in the 2003 observing season aiming at the detection of new objects with planetary transiting companions. Six fields of 35'x35' each located in the Galactic disk were monitored with high frequency for several weeks in February - July 2003. Additional observations of three of these fields were also collected in the 2004 season. Altogether about 800 and 1500 epochs were collected for the fields of both campaigns, respectively.
The search for low depth transits was conducted on about 230000 stars with photometry better than 15 mmag. It was focused on detection of planetary companions, thus clear non-planetary cases were not included in the final list of selected objects. Altogether we discovered 40 stars with shallow (<0.05 mag) flat-bottomed transits. In each case several individual transits were observed allowing determination of photometric elements. Additionally, the lower limits on radii of the primary and companion were calculated. From the photometric point of view the new OGLE sample contains many very good candidates for extrasolar transiting planets. However, only the future spectroscopic follow-up observations of the OGLE sample - determination of the amplitude of radial velocity and exclusion of blending possibilities - may allow to confirm their planetary status. In general, the transiting objects may be extrasolar planets, brown dwarfs, M-type dwarfs or fake transits caused by blending. All photometric data of objects with transiting companions discovered during the 2003 campaigns are available to the astronomical community from the OGLE Internet archive.