WASHINGTON — House Speaker John A. Boehner on Friday appointed seven Republicans to the 12-person committee tasked with continuing investigations into the 2012 attack that killed four Americans in Benghazi, Libya. The move forced Democratic lawmakers to struggle to overcome internal disagreements over how to handle the latest inquiry and whether or not to appoint any of their own members to the new committee.

Mr. Boehner’s announcement came on the House floor before the chamber departed for a weeklong break. In addition to Representative Trey Gowdy of South Carolina, who is chairman of the committee, the speaker appointed Representatives Susan W. Brooks of Indiana; Jim Jordan of Ohio; Mike Pompeo of Kansas; Martha Roby of Alabama; Peter Roskam of Illinois, and Lynn Westmoreland of Georgia. The committee was createdon Thursday on a largely party line vote.

By Friday afternoon, with many lawmakers already on flights back to their districts, the two parties seemed to be at an impasse, with the Republicans forging ahead on a committee that Democratic leaders have called a “kangaroo court.” The disagreement over even the terms of the investigative group — with letters and counterletters pinging back and forth between the leadership offices — underscores the partisan tensions already present in the inquiry.

The attack on the United States’ diplomatic compound in Benghazi on Sept. 11, 2012, has become a cause of the Republican base, which contends that President Obama and the secretary of state at the time, Hillary Rodham Clinton, initially tried to cover up what they knew about the causes of the