Asked about his relationship with President Donald Trump, Tillerson said simply, "Good."
The speculation over Tillerson's remaining in Trump's cabinet came after days of Trump publicly attacking Attorney General Jeff Sessions.
Trump said Sessions had "taken a VERY weak position" on investigating his former opponent in the 2016 presidential election, Democratic nominee Hillary Clinton, over her use of a private email server.
On Monday, Trump called Sessions "beleaguered."
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