"I want them to open their markets like our markets are open", Donald Trump said in the interview that aired Sunday. "I thought very strongly that, you know, the one great thing will happen is the press will start treating me great".
Trump also sought to play down rumors that Mattis could soon leave his administration, saying that the two "get along very well" and calling the Pentagon chief "a good guy". "At some point, everybody leaves".
This marks the first time that the Republican President has publicly said anything negative about Mr Mattis, who last month told reporters not to take seriously reports that he may be leaving.
"It could be that he is" leaving, Trump said of Mattis on the CBS "60 Minutes" program.
He added that he didn't approve of everyone on his Cabinet, telling Stahl that while he thinks he has a "great Cabinet", "there are some people that I'm not happy with". "Something's changing and it'll change back again", he said.
"There have to be consequences. for coming into our country illegally", he said, arguing that "part of the reason, I have to blame myself, the economy is so strong that everybody wants to come into the United States". "People leave. That's Washington".
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"Sure. I know all these things".
The exchange on Mr Mattis came after Mr Trump alluded to upcoming changes in his cabinet, which last week saw the surprise resignation of Nikki Haley, the USA ambassador to the United Nations.
In response to the comments, a Pentagon spokesman said Mr Mattis remained "laser-focused on doing his job".
The Trump administration has experienced an unprecedented turnover rate as compared to past administrations. In a statement after the book's publication, Mattis said that "the contemptuous words about the president attributed to me in Woodward's book were never uttered by me or in my presence". President Trump said the two have "a very good relationship", but suggested there was the possibility he could step down at some point.
Asked about the reports speculating about his departure, Mattis said on September 18: "It's like most of those kinds of things in this town".
Stahl's question was simple: "Why did you have to make fun of her?" Lesley, they treat me worse. "But I don't know that it's man-made".
"But did you have to-" Stahl cut in.