Mr. Obama is also leaning more than ever on his small circle of White House aides, who forged their relationships with him during his 2008 campaign and loom even larger in an administration without weighty voices like those of Robert M. Gates, the former defense secretary, or Hillary Rodham Clinton, the former secretary of state.

Image President Obama tends to hand delicate assignments to his most trusted advisers, like Denis R. McDonough, the White House chief of staff. Credit... Doug Mills/The New York Times

Over the Columbus Day weekend, the White House chief of staff, Denis R. McDonough, traveled to the San Francisco home of Senator Dianne Feinstein, the chairwoman of the Senate Intelligence Committee, to negotiate personally over redactions in a Senate report on the C.I.A.'s detention and interrogation policies after the Sept. 11 terrorist attacks.

That Mr. McDonough would get involved in such an arcane matter puzzles some legislative aides on Capitol Hill, given the other demands on his time. But it testifies to how Mr. Obama tends to hand delicate assignments to his most trusted advisers. Mr. Kerry and Mr. Hagel, meanwhile, are struggling to penetrate the tightly knit circle around the president and carve out a place in the administration.

Mr. Kerry is vocal and forceful in internal debates, officials said, and gets credit for putting together the coalition of Arab states that conducted military strikes in Syria. But he often seems out of sync with the White House in his public statements. White House officials joke that he is like the astronaut played by Sandra Bullock in the movie “Gravity,” somersaulting through space, untethered from the White House.

In separate interviews, Mr. McDonough and Ms. Rice rejected that portrait, saying Mr. Kerry dials into meetings and is heavily involved in the policy process. Aides said a long memo he wrote on the Islamic State has become the playbook for combating the group.

Mr. Hagel has a different problem. A respected former senator, like Mr. Kerry, Mr. Hagel says little in policy meetings and has largely ceded the stage to the chairman of the Joint Chiefs of Staff, Gen. Martin E. Dempsey, who officials said has won the confidence of Mr. Obama with his recommendations of military action against the Islamic State.

Defenders of Mr. Hagel attribute his reticence in meetings to fears that the details will leak into the news media, and say he is more vocal in one-on-one sessions with the president. They also insist that he is more assertive on policy than his reputation suggests, citing a sharply critical two-page memo that he sent to Ms. Rice last week, in which he warned that the administration’s Syria policy was in danger of unraveling because of its failure to clarify its intentions toward President Bashar al-Assad.