Mr. Trump's anger toward Ms. Nielsen, who was sitting several seats to his left at the meeting, was part of a lengthy tirade in which the president railed at his cabinet about what he said was its lack of progress toward sealing the country's borders against illegal immigrants, according to one person who was present at the meeting.
Trump nominated Nielsen to lead the U.S. Department of Homeland Security.
During the meeting, Trump yelled about the United States' porous border and said more needed to be done to fix it.
During the meeting, Trump blamed Nielsen for what he said was her failure to secure USA borders, the newspaper cited the officials as saying.
"The President is rightly frustrated that existing loopholes and the lack of Congressional action have prevented this administration from fully securing the border and protecting the American people", Nielsen's statement said.
The exchange was so hostile, according to The New York Times, that Nielsen later informed colleagues that she planned to leave the administration and drafted a resignation letter, though she did not submit it.
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A Homeland Security spokesperson later denied the claims made in The Times's report: "The [New York Times] article alleging that the Secretary drafted a resignation letter yesterday and was close to resigning is false", spokesperson Tyler Houlton said.
While border apprehensions dipped a year ago to their lowest levels ever, the numbers have been ticking up in recent months, returning to more typical historical levels. "I share his frustration". Nielsen issued a statement Thursday night, but it does not directly address the report or that she came close to resigning.
"We've very much toughened up the border, but the laws are terrible", Mr. Trump said according to the report.
Trump has also been frustrated with Congress's refusal to fully fund his promised border wall along the nation's southern border, and some in the administration had accused DHS leaders of slow-walking more aggressive efforts to separate children from their parents at the border. More recently, however, those numbers have climbed back toward the level they were in the final years of the Obama administration-an intolerable equivalence for Trump. He has also threatened to shut down the government by September 2018 if the Congress does not approve funding to make good on his campaign promise to build a wall on the southern USA border with Mexico.
Just to be clear, Nielsen and the Department of Homeland Security (DHS) under her direction haven't shown any hesitation about separating families.
During his 2016 presidential campaign, Trump fervently pushed for immigration reform by outlining bold plans, including the construction of a massive wall stretching across the US-Mexico border.