WASHINGTON — A House Republican-led investigation of the 2012 terrorist attack on an American diplomatic compound in Benghazi, Libya, will extend well into next year, and possibly beyond, raising concerns among Democrats that Republicans are trying to damage Hillary Rodham Clinton’s presidential prospects.

Representative Trey Gowdy, Republican of South Carolina and the chairman of the House select committee on Benghazi, said his go-slow investigation was not motivated by politics. He said that he had gone out of his way to maintain good relations with Democrats on the committee, asking Representative Elijah Cummings of Maryland, the panel’s ranking Democrat, to join him in private meetings in July with family members of the four Americans killed in Libya in July.

“I promised the family members of the four slain and my colleagues on both sides of the aisle the investigation would be serious and fair,” Mr. Gowdy said in an email. “Nothing would undercut both of those promises like an orchestrated timing.”

But concern is rising, both among Democrats and among those who note that most select committees tend to conclude far more quickly. For instance, the select bipartisan committee to investigate the response to Hurricane Katrina in 2005 took a year from its formation to complete a 361-page report. The bipartisan commission that examined the attacks of Sept. 11, 2001, took a year and a half.