WASHINGTON – As he searches for his fourth Defense secretary in six years, President Obama appears to be looking for a more forceful, articulate military leader to navigate the tough but limited wars that are likely to consume much of his final two years in office.

Finding a candidate with deep Pentagon experience who can help set a coherent strategy and defend it to the public and Congress won't be easy.

Only a day after the job came open, two leading prospects — former Undersecretary of Defense for Policy Michele Flournoy and Sen. Jack Reed, D-R.I. — took themselves out of the running to replace Chuck Hagel, whose departure Obama announced Monday.

That leaves Ashton Carter, who was deputy secretary of Defense from 2011 to 2013, as one of the few contenders with the qualifications Obama appears to be seeking.

A different environment

In his previous two nominees, Obama placed little priority on Defense Department experience, focusing on someone who could oversee the withdrawal of troops from Iraq and Afghanistan. Hagel was a retired Republican senator from Nebraska who was critical of the wars of the past decade, while Leon E. Panetta, who preceded him, had been director of the CIA and had little background in military affairs.

Obama is now facing a different environment. With U.S. forces engaged in military operations in Iraq and Syria, and an incoming Republican majority in the Senate already questioning the administration's handling of the conflicts, he needs a Defense secretary who can explain the strategy to Congress and better direct the military, officials said.

"The president clearly wants someone who can be more forceful and win a public debate defending his policies," said Lawrence J. Korb, a former assistant secretary of Defense who's currently a senior fellow at the Center for American Progress. "He wants someone who looks good on the Sunday talk shows."

Flournoy, who has long been considered a contender for the post, said in a letter to the board of the Center for a New American Security, the think tank she heads, that she asked Obama not to consider her for the post, citing "family considerations," according to a person familiar with the matter. With Flournoy out of the running, a top White House staffer said that Obama was still considering "a number of well-qualified candidates."

Known as bold thinker

White House press secretary Josh Earnest emphasized that Obama was not looking for someone to take the Pentagon in a new direction, but rather to carry out "the strategy that the president has selected." A top priority is dealing with Islamic State militants who have seized control of large parts of Iraq and Syria, Earnest said.

Carter, 60, a theoretical physicist and former Harvard professor, spent years in the Pentagon through two administrations, rising to deputy Defense secretary before leaving last year.

He is known as a bold thinker who understands the Pentagon well and would not likely run into trouble winning Senate confirmation. He was confirmed unanimously by the Senate for both the No. 2 and No. 3. Pentagon positions.

When Carter resigned from the Pentagon in 2013, Sen. John McCain, R-Ariz., praised him lavishly. Now McCain is the incoming chairman of the Senate Armed Services Committee, which will hold hearings on the next Pentagon nominee.

"On many issues relating to defense and national security, Ash and I have had our differences," McCain said at the time. "Some have been profound. But Ash has always conducted himself in a manner that appreciated the valid concerns underlying opposing views."

Obama could also look outside to a candidate like retiring Sen. Carl Levin, D-Mich., chairman of the Senate Armed Services Committee, who isn't as likely to challenge the administration's current policies and is well respected in Congress.

Jeh Johnson, the current Homeland Security secretary and former general counsel for the Pentagon, is also said to be under consideration.