Rep. Mike Rogers, a Republican from Michigan and chairman of the House Intelligence Committee, speaks during an interview in New York on April 8. (Scott Eells/BLOOMBERG)

The organization that represents more than 12,000 FBI special agents on Monday endorsed a Republican congressman to be the bureau’s new leader, as the Obama administration steps up its search for a successor to Director Robert S. Mueller III.

The FBI Agents Association released a statement of support for Rep. Mike Rogers (Mich.), a former agent, and urged President Obama to nominate him when Mueller’s term ends in September.

“His unique and diverse experience as a veteran, FBI agent and member of Congress will allow him to effectively lead the men and women of the bureau,” Konrad Motyka, president of the FBI Agents Association, said in an interview. Motyka said the association’s representatives met with Vice President Biden’s staff about two weeks ago to push for Rogers’s nomination.

Rogers, who has served as chairman of the House Intelligence Committee since 2011, said he was “humbled” by the endorsement of the FBI agents group and would be interested in the job.

“I am honored to have the confidence of the men and women of the FBI’s special agent community,” Rogers said. “The next generation of FBI leadership must recognize how essential special agents are to the bureau’s core mission.”

Rogers joins an unofficial list of people under consideration for the FBI’s top job, according to several current and past administration officials. One of the leading candidates is Lisa Monaco, who oversaw the Justice Department’s National Security Division before becoming Obama’s counterterrorism adviser in March. If chosen, Monaco would be the first woman to head the bureau in its 105-year history.

Other contenders for the job are said to include James B. Comey, deputy attorney general in the George W. Bush administration and Neil H. MacBride, U.S. attorney for the Eastern District of Virginia. Lewis D. Schiliro, a former FBI agent who served in a top post in the bureau’s New York Office and is now a homeland security official in Delaware, has also garnered some support.

Although he enjoys the support of the FBI agents’ organization, Rogers could face political obstacles to a nomination. He has been openly critical of the administration’s handling of counterterrorism investigations, and of Attorney General Eric H. Holder Jr. in some cases.

A Justice Department spokeswoman declined to comment on the search or the people who are being considered.

Officials said the administration wants to find a successor soon so the person can be vetted, nominated and confirmed before Congress goes on summer recess. In the early stages, the process has been coordinated by the Justice Department, but Biden’s office will also be involved in the search.

The next FBI director will take over the agency in the wake of the Boston Marathon bombings, the first large-scale terrorist attack in the United States since Sept. 11, 2001. The new director will also step into an agency with a more complex and demanding mission than the agency Mueller took over just before the Sept. 11 attacks. Mueller had led the bureau’s evolution from a traditional crime-fighting agency to one focused on preventing terrorist attacks.

Motyka said the FBI agents organization believes that Rogers’s background as a former agent sets him apart from the other candidates.

“The best person to lead us is someone who has been inside the organization and has served as an agent,” Motyka said. “Agents are essential to the bureau’s primary mission of protecting our country from a wide array of threats.”

Rogers, a 1985 graduate of Adrian College, was a commissioned officer in the U.S. Army through the Reserve Officers’ Training Corps at the University of Michigan. He was an FBI agent from 1989 to 1994 before being elected to the Michigan Senate in 1995.

Monaco has also served in the FBI, although not as an agent. She worked as a counselor and deputy chief of staff to Mueller in 2007 and served as his chief of staff from 2007 to 2009.