It was shown that run-away electron preionized volume (diffuse) discharge (REP DD) can be used as an excitation source of gas mixtures at elevated pressures and can produce laser emission. We report experimental and simulated results of application of the REP DD for excitation of different active gas mixtures. Kinetic model of the REP DD in mixtures of nitrogen with SF6 is developed allowing predicting the radiation parameters of nitrogen laser at 337.1 nm. Peculiarities of the REP DD development in different gas mixtures are studied, as well. It was shown that the REP DD allows obtaining efficient lasing stimulated radiation in the IR, visible and UV spectral ranges. New operation mode of nitrogen laser is demonstrated under REP DD excitation. Laser action on N2, HF, and DF molecules was obtained with the efficiency close to the limiting value. Promising prospects of REP DD employment for exciting a series of gas lasers was demonstrated. It was established that the REP DD is most efficient for pumping lasers with the mixtures comprising electro-negative gases.