Neutron kinetic energy spectra in coincidence with low-energy $gamma $-ray multiplicities have been measured around $Aapprox $ 110 in the $^{16}$O, $^{20}$Ne + $^{93}$Nb reactions in a compound nuclear excitation energy range of $approx $ 90 - 140 MeV. The excitation energy (temperature) and angular momentum (spin) dependence of the inverse level density parameter $k$ has been investigated by comparing the experimental data with statistical Hauser-Feshbach calculation. In contrast to the available systematic in this mass region, the inverse level density parameter showed an appreciable increase as a function of the excitation energy. The extracted $k$-values at different angular momentum regions, corresponding to different $gamma $-multiplicities also showed an overall increase with the average nuclear spins. The experimental results have been compared with a microscopic statistical-model calculation and found to be in reasonable agreement with the data. The results provide useful information to understand the variation of nuclear level density at high temperature and spins.
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