The resonance states of systems consisting of three identical bosons and three fermions interacting with an attractive 1/r potential are investigated using highly correlated exponential basis functions. The method of complex-coordinate rotation is used to extract energies and widths for the resonances lying below the N = 3 excited state threshold of the respective two-body subsystem. We have obtained a total of 24 S-wave resonances for the three-boson system and a total of 19 S-wave resonances in total spin-3/2 (the 4S state) and a total of 15 S-wave resonances in total spin-1/2 (the 2S state) below the N = 3 threshold. For the resonances associated with the N = 3 threshold, we have obtained two, three and four series of Rydberg states for the three-boson system, three-fermion system for 2S states and three-fermion system for 4S states, respectively. The resonance energies and widths of these states for the three-body self-gravitating bosons and fermions are reported.