“I think he has it all wrong,” Mr. Negroponte said.

It is a view shared by many at the State Department who have long hoped that Mr. Tillerson would help imbue their work with the kind of larger purpose for which many joined the Foreign Service. John Kerry, Mr. Tillerson’s predecessor, exhorted them to save the planet from climate change. Condoleezza Rice charged them with fulfilling the human yearning for freedom and democracy.

Mr. Tillerson wants to fix their email system.

“That’s why we call it a process redesign,” he said Thursday, using the kind of management talk rarely uttered by the nation’s chief diplomat.

To be sure, the flights of rhetoric of Mr. Tillerson’s predecessors sometimes fell with a thud. And the State Department’s email system is truly horrible, having entirely crashed recently for most of a day.

But employees yearn to be part of something bigger than a bureaucratic Gordian knot, and Mr. Tillerson rarely even tries to speak of a larger purpose.

The capital “B” in his letter to employees referred to billions of dollars. Even so, such a plan would deliver far fewer savings, spread out over a much longer period of time, than Mr. Tillerson’s own budget plan initially envisioned, which will be greeted with some relief both in the department and on Capitol Hill.

Members of Congress have complained that Mr. Tillerson has given them almost no details of his plans, and a spending blueprint passed last week by a crucial Senate committee largely rejected Mr. Tillerson’s proposed cuts, with a bipartisan group of senators saying that now was not the time to retreat from diplomacy.

Mr. Tillerson must provide the White House with an outline of his redesign by Friday, although he has said that the full details will most likely not be available until the end of the year, with implementation beginning next year.