To provide a fluorinated elastic copolymer having high crosslinkability, having high flowability and excellent in the compression set and the resistance to bases, and its production process.A process for producing a fluorinated elastic copolymer, which comprises copolymerizing (a) tetrafluoroethylene and (b) propylene and as the case requires, (c) a perfluoro(alkyl vinyl ether) in the presence of an iodine compound represented by the formula RI2 (wherein R is a hydrocarbon group or perfluoroalkyl group having at least 3 carbon atoms) at a temperature of from 0° C. to 50° C., and a fluorinated elastic copolymer obtained by the production process.