A non-flammable quasi-solid electrolyte and a rechargeable non-lithium alkali metal cell containing this electrolyte. The electrolyte comprises an alkali metal salt dissolved in an organic liquid solvent with a concentration higher than 2.5 M (preferably >3.5 M) or a molecular ratio greater than 0.2 (preferably >0.3), wherein the alkali metal is selected from Na, K, a combination of Na and K, or a combination of Na and/or K with Li. The alkali metal salt concentration is sufficiently high so that the electrolyte exhibits a vapor pressure <0.01 kPa when measured at 20° C., a vapor pressure <60% of the vapor pressure of thet organic solvent when measured alone, a flash point at least 20 degrees Celsius higher than a flash point of the organic liquid solvent when measured alone, a flash point higher than 150° C., or no detectable flash point.