A senior administration official confirmed the incident to Reuters, saying: "He lit into her."
A DHS spokesman said in a statement on Thursday that the New York Times story "alleging that the Secretary drafted a resignation letter yesterday and was close to resigning is false."
Nielsen "is hard at work today on the President's security-focused agenda and supporting the men and women of @DHSgov," he added.
The White House declined specific comment on whether Trump berated Nielsen, her supposed resignation letter and on whether Trump retained confidence in Nielsen, who took over at DHS in December.
"The president is committed to fixing our broken immigration system and our porous borders. We are a country of laws and the president and his administration will enforce them," White House spokeswoman Sarah Sanders said in a statement on Thursday.
Nielsen, in a statement on Thursday, said she shared Trump's frustration that "existing loopholes and the lack of Congressional action have prevented this administration from fully securing the border and protecting the American people."
"These are complex issues and I will continue to direct the Department to do all we can to implement the President's security-focused agenda," she added, without saying anything about resignation plans.
Nielsen is in charge of the 20,000 border agents who work at Immigration and Customs Enforcement.
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.
Trump has become frustrated in recent weeks over growing numbers of illegal border crossings after a drop during his first year in office, the Times said, citing several officials.
Trump believes Nielsen and other DHS officials are resisting directives that parents be separated from their children when families cross illegally into the United States, to deter them from entering, the newspaper said, citing the officials.
Trump's hard line against illegal immigration is a centerpiece of his presidency as he pursues an "America First" agenda that includes a proposed wall along the U.S.-Mexico border, saying it was needed to stem the flow of immigrants and drug trafficking.