An experimental study of laser driven electron acceleration in N2 and N2-He mixed gas-jet targets using laser pulses with durations of ∼60–70 fs is presented. Generation of relativistic electron beams with quasi-thermal spectra was observed at a threshold plasma density of ∼1.6 × 1018 cm−3 in the case of pure N2. The threshold density was found to increase with increasing doping concentrations of He. At an optimum fraction of 50% of He in N2, generation of quasi-monoenergetic electron beams was observed at a comparatively higher threshold density of ∼2 × 1018 cm−3, with an average peak energy of ∼168 MeV, average energy spread of ∼21%, and average total beam charge of ∼220 pC. The electron acceleration could be attributed to direct laser acceleration as well as the hybrid mechanism. The observation of an optimum fraction of He in N2 (in turn threshold plasma density) for comparatively better quality electron beam generation can be understood in terms of the plasma density dependent variation in the dephasing rate of electrons with respect to the transverse oscillating laser field. Results are also supported by 2D particle-in-cell simulations performed using the code EPOCH.