WASHINGTON — President Trump made no immediate moves on Friday to dismiss members of his administration, despite continuing reports of an impending shake-up that have unsettled the White House.

Two embattled cabinet secretaries — Ben Carson at the Department of Housing and Urban Development and David Shulkin at the Department of Veterans Affairs — remained in their posts despite speculation that they would be replaced because of the president’s unhappiness with their use of public funds.

John F. Kelly, the White House chief of staff, met at the White House with Mr. Carson on Friday morning, but no announcement was made about Mr. Carson’s future or Mr. Shulkin’s.

There have also been conflicting indications that Mr. Trump — at some point — intends to fire Lt. Gen. H. R. McMaster, his second national security adviser, after the dismissal this week of Secretary of State Rex W. Tillerson.