The aim of this paper is to provide a measurement of the mass accretion rate in a large, complete sample of objects in the core of the star forming region rho Oph. The sample includes most of the objects (104 out of 111) with evidence of a circumstellar disk from mid-infrared photometry; it covers a stellar mass range from about 0.03 to 3M_{sun}_ and it is complete to a limiting mass of ~0.05M_{sun}_. We used J and K-band spectra to derive the mass accretion rate of each object from the intensity of the hydrogen recombination lines, Pa{beta} or Br{gamma}. For comparison, we also obtained similar spectra of 35 diskless objects.