Mr Trump's alleged comments came after he was told 15,000 Haitians had received visas to enter the USA since he became President.
The president lamented that more than 2,500 recipients were from Afghanistan, expressing concerns about terrorism.
He then reportedly said 40,000 had come from Nigeria and would never "go back to their huts" once they had seen America.
Press Secretary Sarah Sanders shot down the "outrageous claims", stating that senior officials who were in the meeting refuted them. In a shocking story Saturday, The New York Times cited two sources who described in explicit terms how Trump has raged against his advisers for not doing more to translate his nativist politics into policy.
Several other people who attended the meeting also told The Times they did not recall the comments, but the two officials who described them found them so significant they told others about them at the time.
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Tillerson was reportedly frustrated by Trump's anger and accusations, but the president was backed up by his nativist adviser Stephen Miller and his chief of staff John Kelly, who, later in the year, unapologetically lied about and defamed Frederica Wilson, a prominent African-African congresswoman from Florida.
Haiti sent 15,000 people. If he was so bad at his job, maybe he should stop issuing visas altogether, Mr. Tillerson fired back.
"Tempers flared and Mr. Kelly asked that the room be cleared of staff members", they continued.
According to the report, "friends were calling to say he looked like a fool, Mr. Trump said", as "so many foreigners had flooded into the country since January".
Trump's effort to change USA immigration policy has been a disorderly and sometimes dysfunctional process, the Times story noted, but even as he has been frustrated by the limits on presidential power, his plans have gained increasing momentum as the White House became more disciplined. "Slowed it, stopped it, begun to turn it around and started sailing in the other direction". "He's come into office with an aggressive strategy of trying to reverse the demographic changes underway in America".