Tillerson, Corker said, "is in a very frustrating place" where "he ends up not being supported in a way I hope a secretary of state would be supported".
President Donald Trump says he still has confidence in his secretary of state and did not intend to "undercut" him when he questioned his intelligence level.
The public back and forth has laid bare the fraught Trump-Tillerson relationship, making Tuesday's meetings possibly high stakes - if not awkward - affairs.
"This is what I don't understand about Washington", Tillerson said on Wednesday. "They're a little overheated right now, and I think we need to calm them down first".
Trump called the report "Fake News" in a tweet. "And I can tell you who is going to win", Trump told Forbes.
State Department officials did not immediately respond to requests for comment. Trump tweeted early Tuesday morning in the US.
He said that reaching out to congressional Democrats for help in getting immigration legislation passed is hard because "the Democrats don't want secure borders". Clearly Mr Trump doesn't agree.
Speaking at a press conference in Beijing, Tillerson said the U.S. made it clear through its direct channels to North Korea that it was seeking peace through talks.
"As the secretary of state said, this is a pretty ridiculous accusation and, frankly, I think it's beneath the secretary of state to weigh in on every rumor out there", Huckabee Sanders said. He also copped a backhander from his president today. The NFL gave up its federal tax-exempt status a couple years ago and now files tax returns as a taxable entity. After The New York Times detailed decades of sexual harassment allegations against Weinstein, the company he co-founded fired him, he noted, "forcing them to change their name from The Weinstein Company to something more positive, Asbestos Child Slappers Inc".