The department has released thousands of pages of the emails — which were housed on a private server in Mrs. Clinton’s home — on the last day of each month and is supposed to complete the disclosure by Jan. 29.

The emails posted Thursday provided a further glimpse into the cloistered and sometimes caustic world of Mrs. Clinton’s entourage during her four-year stint as the nation’s top diplomat. On display once again were the rivalries and insecurities in her circle as she represented to the outside world the man who beat her for the presidency.

One ally confided to her that Chancellor Angela Merkel of Germany did not care for “the Obama phenomenon,” while another urged immediate aid to Libya if Col. Muammar el-Qaddafi were to fall, as he later did. Some of her advisers did little to hide their disdain for President Obama’s aides, while Mrs. Clinton herself fretted about reports that she did not exercise enough influence in the White House. “Pls go through my schedules and count my visits to refute this and correct record,” Mrs. Clinton wrote an aide in response to a “ridiculous column” on the number of times she had visited the White House.

Subordinates and outsiders lavished praise on her. Henry A. Kissinger, perhaps her most famous living predecessor, wrote in 2012 seeking help to declassify some of his papers, ending with this handwritten note: “I greatly admire the skill and aplomb with which you conduct our foreign policy.”

The sometimes byzantine nature of Mrs. Clinton’s orbit was summed up in one email from Philippe Reines, who designed an irreverent flow chart to determine who should ride in her limousine while she traveled abroad. “Ambassador Tolerable?” one entry asked. If yes, he or she got to ride in the car. If not, Mrs. Clinton would ride without the intolerable envoy.