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Mr. Romney countered President Obama’s claim that he outsourced jobs overseas as governor of Massachusetts, saying that the Democrat is twisting facts and hiding blemishes on his own record.

Speaking at a town-hall style meeting in Grand Junction, Colo., Mr. Romney said that independent fact checkers have called Mr. Obama’s attacks against him both “false and misleading.”

“But it is interesting that when it comes to outsourcing that this president has been outsourcing a good deal of American jobs himself by putting money into energy companies — solar and wind — that end up making their products outside the United States,” he said. “If there is an outsourcer-in-chief, it is the president of the United States, not the guy who is running to replace him.”

Mr. Obama and Democrats have touted a report in The Washington Post that said some of the businesses that Mr. Romney’s former company Bain Capital invested in outsourced American jobs to cut costs.

Republicans and the Romney camp are now trying to turn the tables, pointing to a more recent report in the Washington Post in which Mr. Obama record on outsourcing also comes under fire.

Seth McLaughlin contributed to this report.