Fiat said Thursday it has expanded its controlling stake in Chrysler Group, meeting the final target set by the U.S. government in the deal that rescued the U.S. carmaker from bankruptcy and taking a step toward a planned merger. Fiat’s holding increased to 58.5 percent from 53.5 percent after the carmakers committed to produce a fuel-saving model in the United States, the companies said. Fiat ended up paying about $2 billion for the holding in the third-largest U.S. automaker. The higher stake “represents repayment of the trust placed in Fiat to introduce its fuel-efficient cars and engines to the U.S. market,’’ Sergio Marchionne, chief executive officer of Chrysler and Turin, Italy-based Fiat, said in a statement. “The acquisition of a further 5 percent of Chrysler is a fundamental step in completion of the integration between our two groups.’’