In an interview with CNN on Friday, Tillerson said he intends to remain in his role serving the president through 2018.
"The State Department gets stronger every day," Tillerson told CNN. "And I look forward to having a very, very successful 2018."
He also said that Trump has given him no indication that his job might be threatened, CNN reported.
The rumors of an acrimonious relationship, including a report by NBC News in October that Tillerson had called Trump a "moron" during a Pentagon meeting, were rekindled by leaked excerpts from author Michael Wolff's new book, "Fire and Fury."
Tillerson, responding to Wolff's salacious look inside the first year of the Trump presidency, said he "never questioned [the president's] mental fitness."