The president made the comments in an interview with Forbes, speaking about the report that Tillerson called him a "moron" over the summer.
"I think it's fake news, but if he did that, I guess we'll have to compare IQ tests. And I can tell you who is going to win," Trump said.
Following up an earlier question on the matter, Kristen Welker of NBC News asked Sanders how the president can expect the secretary of state to be effective when he's "questioning his intelligence."
"He wasn't questioning the secretary of state's intelligence," Sanders answered. "He made a joke. Maybe you guys should get a sense of humor and try it sometime," said Sanders.
She said Trump has complete confidence in Tillerson, accusing the media of continuing to bring up a non-story.
"You guys want to talk about who likes who. That's not what we're doing here," Sanders said.
Tillerson held a news conference last week in which he praised Trump and affirmed his commitment to the administration. But he declined to specifically address whether he made the "moron" remark.
Watch the exchange above.