The Republican-led Armed Services Committee backed a nonbinding resolution that disapproves of the exchange and faults Obama for failing to notify Congress 30 days in advance of the May swap, as required by law.
The vote was 34-25 with two Democrats Reps Tulsi Gabbard of Hawaii and Mike McIntyre of North Carolina joining Republicans in support of the measure yesterday.
The resolution also raises national security concerns about the transfer of the Taliban while expressing relief that Bergdahl has returned safely to the United States.
The Obama administration has come under harsh criticism from many in Congress, especially Republicans, who have said Bergdahl was a deserter and the United States gave up too much for his freedom. Several lawmakers have cited intelligence suggesting the high-level Taliban officials could return to the Afghanistan battlefield.
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Five senior Taliban were released from detention at Guantanamo Bay, Cuba, in exchange for Bergdahl, who had disappeared from his post in Paktika province in eastern Afghanistan on June 30, 2009. The five Taliban are to remain in Qatar for a year.
The Joint Chiefs of Staff unanimously supported the exchange, insisting that the United States has a sacred commitment to men and women who serve that it will never leave anyone behind on the battlefield.
Army Gen Martin Dempsey, the chairman of the Joint Chiefs, said the swap in May was "likely our last, best opportunity" to free Bergdahl.
Republicans on the Armed Services panel accused Obama of breaking the law, with Rep Trent Franks, referring to a "lawless presidency" in which the president has failed to live up to his oath of office.
The House will be voting on the lawsuit this week.