The near-Earth objects with low-Jovian Tisserand invariant (TJ) represent about 9 per cent of the known objects orbiting in the near-Earth space, being subject of numerous planetary encounters and large temperature variations. We aim to make a spectral characterization for a large sample of NEOs with TJ ≤ 3.1. Consequently, we can estimate the fraction of bodies with a cometary origin. We report new spectral observations for 26 low-TJ NEOs. The additional spectra, retrieved from different public data bases, allowed us to perform the analysis over a catalogue of 150 objects. We classified them with respect to Bus-DeMeo taxonomic system. The results are discussed regarding their orbital parameters. The taxonomic distribution of low-TJ NEOs differs from the entire NEOs population. Consequently, TJ ~ 3 can act as a composition border too. We found that 56.2 per cent of low-TJ NEOs have comet-like spectra and they become abundant (79.7 per cent) for TJ ≤ 2.8. 16 D-type objects have been identified in this population, distributed on orbits with an average TJ = 2.65 ± 0.6. Using two dynamical criteria, together with the comet-like spectral classification as an identification method and by applying an observational bias correction, we estimate that the fraction of NEOs with a cometary nature and H ∈ (14, 21) mag has the lower and upper bounds (1.5 ± 0.15) and (10.4 ± 2.2) per cent. Additionally, our observations show that all extreme cases of low-perihelion asteroids (q ≤ 0.3 au) belong to S-complex.