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Results from DROXO. III. Observation, source list and X-ray properties of sources detected in the "Deep Rho Ophiuchi XMM-Newton Observation"

X-rays from very young stars are powerful probes to investigate the mechanisms at work in the very first stages of the star formation and the origin of X-ray emission in very young stars. We present results from a 500 ks long observation of the Rho Ophiuchi cloud with a XMM-Newton large program named DROXO, aiming at studying the X-ray emission of deeply embedded Young Stellar Objects (YSOs). The data acquired during the DROXO program were reduced with SAS software, and filtered in time and energy to improve the signal to noise of detected sources; light curves and spectra were obtained. We detected 111 sources, 61 of them associated with rho Ophiuchi YSOs as identified from infrared observations with ISOCAM. Specifically, we detected 9 out of 11 Class I, 31 out of 48 Class II and 15 out 16 Class III objects. Six objects out of 21 classified Class III candidates are also detected. At the same time we suggest that 15 Class III candidates that remain undetected at log Lx < 28.3 are not related to the cloud population. The global detection rate is ~64%. We have achieved a flux sensitivity of ~5 x 10^{-15} erg s^{-1} cm^{-2}. The Lx to L_bol ratio shows saturation at a value of ~ -3.5 for stars with T_eff <= 5000 K or 0.7 M_sun as observed in the Orion Nebula. The plasma temperatures and the spectrum absorption show a decline with YSO class, with Class I YSOs being hotter and more absorbed than Class II and III YSOs. In one star (GY 266) with infrared counterpart in 2MASS and Spitzer catalogs we have detected a soft excess in the X-ray spectrum which is best fitted by a cold thermal component less absorbed than the main thermal component of the plasma. Such a soft component hints to the presence of plasma heated by shocks due to jets outside the dense circumstellar material.