 -- The State Department is pushing back on a new wave of rumors that Secretary of State Rex Tillerson is planning on resigning.

“That is false,” spokesperson Heather Nauert said when asked about the rumors at the department's briefing Tuesday. “The secretary has been very clear: He intends to stay here at the State Department. We have a lot of work that is left to be done ahead of us. He recognizes that. He’s deeply engaged in that work.

“He does, however, serve at the pleasure of the president, just as any Cabinet official,” she added, in what could be taken as a nod to the president’s open criticism of Attorney General Jeff Sessions and speculation that he might resign, too.

Tillerson has had some tension with the White House over staffing at the State Department and his independence to make decisions about the nation’s foreign policy agency, senior administration officials told ABC News. But he's also remarked about his commitment to service and the call he heard to take this role.

“I’m still developing myself as a values-based servant leader, and this new opportunity that I have to serve our country has provided me with new ways of learning ... so it gives me a chance to grow as a leader,” he told the Boy Scouts of America in an emotional address Friday.

Senior aide R.C. Hammond has said Tillerson will stay in the role as “as long as there are rogue regimes pursuing nuclear weapons or terrorists seeking safe haven,” according to Buzzfeed News.

Tillerson has also been out of the public eye since Friday, and Nauert said today that he’s “taking a little time off.”

“He does have the ability to go away for a few days on his own ... just taking a little time off," she said. “He’s got a lot of work. He just came back from that mega-trip from overseas -- as you all well know, many of you were there for the G-20, and his other travel as well, so he’s entitled to taking a few days himself.”

She later clarified that the vacation was planned in advance and was not in response to any resignation rumors.

It is customary to list “no public appointments” when a secretary is on a personal vacation, according to The Associated Press. But the State Department has been releasing empty public schedules for Tillerson for a few days now, with no details on what he is doing other than “meetings and briefings.”

Last Thursday, he met with the president, Defense Secretary James Mattis, Chairman of the Joint Chiefs of Staff Gen. Joseph Dunford and other top officials at the Pentagon, before briefing members of the House of Representatives on Capitol Hill; meanwhile, his public schedule listed only “meetings and briefings” at the State Department.

Nauert also spoke to Tillerson’s thoughts on Trump’s politically charged speech to the Boy Scouts –- just three days after Tillerson’s own. Nauert said that Trump addressed the Boy Scouts Jamboree at Tillerson’s invitation, but the secretary could not attend.

Tillerson is “aware of the president’s comments,” but didn’t express an opinion on what he said, according to Nauert.

ABC News' Jordan Phelps contributed to this report.