WASHINGTON — Shortly after President Obama announced the resignation of Defense Secretary Chuck Hagel at the White House on Monday, he walked over to a meeting of his entire National Security Council staff, where he told the embattled group that they were critical to an ambitious foreign policy agenda.

The timing was a coincidence, but it seemed an unmistakable sign that Mr. Hagel’s departure does not portend a broader internal shake-up. If anything, it may represent the final triumph of a White House-centric approach to national security.

Mr. Obama does not appear likely to replace his national security adviser, Susan E. Rice, who skirmished with Mr. Hagel over Syria policy and others. Nor is he mulling a change in his chief of staff, Denis R. McDonough, who has exerted heavy influence over foreign policy, at times acting almost as a shadow national security adviser.

With his core team intact, and with none of the candidates to succeed Mr. Hagel likely to show the independence of Mr. Obama’s first defense secretary, Robert M. Gates, the White House seems likely to keep a tight leash on foreign policy for the remainder of Mr. Obama’s presidency.