WASHINGTON — Pressure is mounting on the leaders of the Centers for Disease Control and Prevention — from inside and outside the agency — to speak publicly against the White House’s manhandling of C.D.C. research and public health decisions, with career scientists so demoralized they are talking of quitting if President Trump wins re-election.

The situation came to a boiling point this week when William H. Foege, a giant in public health who led the C.D.C. under Democratic and Republican presidents, called for its current director, Dr. Robert R. Redfield, to “stand up to a bully” — he meant Mr. Trump — even at the risk of being fired.

“Silence becomes complicity,” he said in an interview, after a private letter he wrote to Dr. Redfield leaked to the news media.