President Donald Trump reportedly grew enraged at a June meeting over the amount of visas awarded to travelers from certain countries, grumbling that 15,000 Haitians who entered the United States in the preceding months "all have AIDS" and that the 40,000 Nigerian visitors would never "go back to their huts" in Africa.
The Times reported the president also complained about the 40,000 people who had come from Nigeria, saying they would never "go back to their huts" in Africa after being in the USA, based on two officials' accounts.
Mr Trump's alleged comments came after he was told 15,000 Haitians had received visas to enter the U.S. since he became President. The New York Times attributes the quote to an anonymous source and another unnamed person told of the comment by someone else at the meeting.
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.
According the sources, when Trump learned 15,000 people from Haiti had been granted U.S. visas, he remarked: "They all have AIDS".
The story is titled "Stoking Fears, Trump Defied Bureaucracy to Advance Immigration Agenda" and takes a look at what the president has done to push his hard-line stances.
The White House issued a swift denial of the comments on Saturday, calling the claims made by the Times "outrageous".
More than 2,500 were from Afghanistan, a terrorist haven, the president complained.
The Times reported that Tillerson replied angrily that "if he was so bad at his job, maybe he should stop issuing visas altogether".
The Times report said Trump has long held contempt for immigrants, which is likely a surprise to few. "He's come into office with an aggressive strategy of trying to reverse the demographic changes underway in America".
The White House is said to have confirmed the meeting.
The New York Times cited anonymous sources who told its reporters' they were either there when the comments were allegedly made or had been told about the remarks by others present.