We present low-resolution (R=900) optical (576.1-1051.1 nm) spectroscopic observations of 40 candidate very low mass members in the Upper Scorpius OB association. These objects were selected using the I, J, and K photometry available in the Deep Near-Infrared Survey (DENIS) database. We have derived spectral types, and we have measured Hα and Na I doublet (at 818.3 and 819.5 nm) equivalent widths. We assess the youth of the objects by comparing them with their older counterparts of similar spectral type in the Pleiades cluster and the field. Our analysis indicates that 28 of our targets are young very low mass objects, and thus they are strong candidate members of the OB association. The other 12 DENIS sources are foreground M dwarfs or background red giants. Our sample of spectroscopic candidate members includes 18 objects with spectral types in the range M6.5-M9, which are likely young brown dwarfs. We classify these candidates as accreting/nonaccreting using the scheme proposed by Barrado y Navascués & Martín. We find five substellar-mass candidate cluster members that are still undergoing mass accretion, indicating that the timescale for accretion onto brown dwarfs can be as long as 5 Myr in some cases. Based on observations obtained with the ESO New Technology Telescope.