The president's eruption was witnessed by Cabinet members plus a number of senior White House officials - including counselor Kellyanne Conway, advisers Jared Kushner and Ivanka Trump, press secretary Sarah Huckabee Sanders, immigration adviser Stephen Miller and chief economic adviser Larry Kudlow.
Nielsen, who is a protegee of John Kelly, the White House chief of staff, has drafted a resignation letter but has not submitted it, according to two of the people. DHS oversees U.S. Customs and Border Protection.
She added that "border security is the most basic and necessary responsibility of a sovereign nation" and said she would "continue to direct the department to do all we can to implement the president's security-focused agenda".
Trump, she told the Times, is "rightly frustrated that existing loopholes and the lack of congressional action have prevented this administration from fully securing the border".
One person at the meeting said Trump railed at the whole Cabinet over what he said was its lack of progress in keeping out illegal immigrants, the Times said.
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Nielsen did not deny the meeting had grown heated in a statement Thursday evening, but said she shared the president's frustrations. The Times report claimed that she was "miserable" in her job according to a "person close to Ms. Nielsen". The president's anger was stoked by Attorney General Jeff Sessions, who remarked that the Department of Homeland Security could just arrest people at the border, the source said.
The Trump administration, under U.S. Secretary of Homeland Security Kirstjen Nielsen, has moved to revoke this special status and to expel tens of thousands of protected immigrants. I share his frustration. 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. Trump went on a Twitter tear, writing that he'd told Nielsen to block the migrants from entering the U.S.
Trump has clashed with Nielsen for weeks.
"We'll work in conjunction with the governors who are in fact on the front lines to see what they need and work it within the National Guard", Nielsen told reporters during a White House Press briefing at the time.
In Sept. 2017, the president openly expressed disdain over Sessions' decision to recuse himself from all investigations relating to Russian Federation and even said he would have chosen another person for the job had he known Sessions would make that decision.
One persistent issue has been Trump's belief that Nielsen and other officials in the department were resisting his direction that parents should be separated from their children when families cross illegally into the United States, several officials said.