Turkey's foreign minister, Mevlüt Çavuşoğlu, told reporters immediately ahead of his meeting with Tillerson that the move is "a grave mistake".
President Donald Trump tweeted on Friday that reports he would soon fire Secretary of State Rex W. Tillerson were "fake news", and that "I call the final shots".
But Tillerson retorted: "This is a narrative that keeps coming up every six weeks, and I would say you all need to get some new sources, because your story keeps being wrong".
Asked if some at the White House wanted him to resign, Tillerson told reporters: "It's laughable ... laughable".
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Tillerson's relationship with Trump has been strained by the top USA diplomat's softer line on North Korea and other policy differences, as well as by reports in October that he had called the president a "moron".
U.S. Secretary of State Rex Tillerson is planning a trip to Africa in the first three months of next year, a senior aide said on Wednesday, amid speculation how long Tillerson might stay in the job. U.S. Republican Senator Tom Cotton, one of Trump's staunchest defenders in Congress, would be tapped to replace Pompeo at the Central Intelligence Agency, officials said.
Secretary of State Rex Tillerson met USA military officers on Wednesday to prepare for a trip to better coordinate American security and diplomatic strategy in Africa. At the European Union and North Atlantic Treaty Organisation this week, Tillerson espoused a more traditional USA foreign policy, defending the Iran nuclear deal agreed by world powers in 2015, warning of a more assertive Russian Federation and saying he had become "quite close" with Germany's foreign minister Sigmar Gabriel.