We demonstrate transverse-magnetic (TM) dominant deep-ultraviolet (DUV) stimulated emission from photo-pumped AlGaN multiple-quantum-well lasers grown pseudomorphically on an AlN/sapphire template by means of photoluminescence at room temperature. The TM-dominant stimulated emission was observed at wavelengths of 239, 242, and 243 nm with low thresholds of 280, 250, and 290 kW/cm2, respectively. In particular, the lasing wavelength of 239 nm is shorter compared to other reports for AlGaN lasers grown on foreign substrates including sapphire and SiC. The peak wavelength difference between the transverse-electric (TE)-polarized emission and TM-polarized emission was approximately zero for the lasers in this study, indicating the crossover of crystal-field split-off hole and heavy-hole valence bands. The rapid variation of polarization between TE- and TM-dominance versus the change in lasing wavelength from 243 to 249 nm can be attributed to a dramatic change in the TE-to-TM gain coefficient ratio for the sapphire-based DUV lasers in the vicinity of TE-TM switch.