The generation of relativistic electron beams with quasi-thermal energy distribution (maximum energy: 30 MeV) by the interaction of a Ti:sapphire laser pulse of 200 fs duration, focussed to an intensity of ∼2.1 × 1018 W cm−2, with an underdense (electron density ∼3.6 × 1019 to ∼1.1 × 1020 cm−3) He gas-jet plasma was observed. We observed two stages of self-focusing of the laser pulse in the plasma. Two groups of accelerated electrons associated with these two stages of laser channeling were also observed, and are attributed to the betatron resonance acceleration mechanism. This is supported by 2D PIC simulations performed using the EPOCH code and a detailed theoretical analysis. Further, the generation of quasi-monoenergetic (ΔE/E ∼ 10%–20%) electron beams with a peak energy of ∼17–22 MeV was also observed, even with such long laser pulses, although with a low probability of occurrence.