Tillerson signed a counterterror agreement with Qatar this week and called on all sides to negotiate, with his top aide telling the press in regard to all countries involved in the crisis, "No one's hands are clean here."
"If we ever had to leave, we would have 10 countries willing to build us another one, believe me, and they will pay for it," the president said.
The UAE and Saudi Arabia have been lobbying for just that, to host a U.S. base as a way to weaken Qatar's ties to the U.S.
Although Trump concluded in the interview that, "We are going to have a great relationship with Qatar," his comments on the military base stood in contrast to Mattis’ assertion later in the week that, "There's no need to look at alternatives" to the Qatar base because "right now we've had no impact on our military operations."
Tillerson told reporters on the flight home from the Gulf that he saw some progress toward ending the impasse. He said he and his team "brought ideas on paper and then facilitated a lot of discussion around that," laying out a path for both sides on how they might address areas of disagreement and calling on them to sit down together to do so.
"In my view, there's a changed sense of willingness to at least be open to talking to one another," Tillerson said, adding, "The final and ultimate resolution may take quite a while."
But after the top U.S. diplomat left the region, the UAE state minister for foreign affairs went on a tweetstorm in Arabic, saying the rift is "far from a political solution" and that the countries face a "long estrangement." He even seemed to welcome the possibility of a future with no ties to Qatar at all: "Although we may lose the confusing and confused neighbor with its own social fabric, we will be gaining clarity and transparency."