Trump was fuming after Kelly's Fox News interview, a source familiar with the matter told CNN, adding that the President "hated" the comments.
"The Wall is the Wall, it has never changed or evolved from the first day I conceived of it. Parts will be, of necessity, see through and it was never intended to be built in areas where there is natural protection such as mountains, wastelands or tough rivers or water," the President tweeted.
"The Wall will be paid for, directly or indirectly, or through longer term reimbursement, by Mexico, which has a ridiculous $71 billion dollar trade surplus with the U.S. The $20 billion dollar Wall is "peanuts" compared to what Mexico makes from the U.S. NAFTA is a bad joke!"
Later Thursday, Trump insisted that his relationship with his chief of staff is fine.
"He's great," the President told reporters during a stop in Pittsburgh. "I think he's doing a great job. I think General Kelly is doing a really great job. He's a really special guy."
Asked if he had a problem with what Kelly said to members of Congress -- that Trump's views on immigration were "uninformed" during the campaign -- the President replied, "No, he didn't say that. Well, I don't think he said it the way you would like him to say it. He's doing a terrific job."
Appearing on Fox News Wednesday evening, Kelly pointed to the border wall as an example of how the President has adjusted his views after being briefed by experts.
"He has evolved in the way he's looked at things," Kelly said, adding, "Campaign to governing are two different things, and this President has been very, very flexible in terms of what is within the realm of the possible."
He added, "He's changed his attitude towards the DACA issue and even the wall."
Asked whether Mexico would pay for the wall, Kelly suggested the payment would be indirect.
"We have some ideas on how things like visa fees, renegotiation on NAFTA on what that would mean to our economy. So in one way or another, it's possible that we could get the revenue from Mexico but not directly from their government," he told Fox.
Sources also told CNN
that Kelly told Democratic lawmakers that some of Trump's positions on the border wall were "uninformed."
Trump's tweets Thursday mark the latest example of him contradicting his own administration officials or White House policy. He publicly suggested
last fall that Secretary of State Rex Tillerson was "wasting his time" trying to negotiate with North Korea, and last week complicated
a closely coordinated effort between his administration and congressional Republican leadership on a six-year extension of a section of the Foreign Intelligence Surveillance Act.
From December 2016 through November 2017, the United States ran a trade deficit of $70.1 billion with Mexico, according to the Commerce Department. That figure represents goods only -- things like cars, oil and food.
Including services, the trade deficit with Mexico was $68.3 billion from October 2016 through September 2017, the most recent figures available. This includes things like tickets on US airlines, US banking services and US media services.