ABSTRACT Recent observational studies of the Galactic bulge by APOGEE have revealed that about 1 per cent of the bulge stars have rather high nitrogen abundances ([N/Fe] > 0.5). We here numerically investigate in what physical conditions these N-rich stars (NRSs) can be formed in spherical and discy stellar systems with stellar masses of $10^7\!-\!10^9 \, {\rm M}_{⊙ }$ that are the bulge’s building blocks. The principal results are as follows. A large fraction (>0.5) of new stars formed from interstellar medium polluted (ISM) by ejecta of asymptotic giant branch stars can have [N/Fe] > 0.5 within stellar systems, if the gas mass fraction of ISM (fg) is low (≤0.03). The mass fraction of NRS among all stars (fnrs) can be higher than ≈1 per cent within ≈0.5 Gyr time-scale of star formation, if the mean stellar densities (ρs) of the systems are higher than $≈ 0.1 \, {\rm M}_{⊙ }$ pc−3. The [N/Fe] distributions depend on ρs, fg, and age distributions of their host stellar systems. NRSs have compact and discy spatial distributions within their host systems and have rotational kinematics. Based on these results, we propose that the vast majority of the bulge’s NRSs originate not from globular clusters (GCs) but from its high-density building blocks. We suggest that NRSs in the Galactic stellar halo have the same origin as those in the bulge. We also suggest that low-density dwarf spheroidal and gas-rich dwarfs are unlikely to form NRSs. GCs are not only the formation sites of NRS.