To accomplish the idea he floated on Tuesday, Mr. Trump would have to find a way around the 14th Amendment to the Constitution, which states, “All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the State wherein they reside.”

The amendment means that any child born in the United States is considered a citizen. Amendments to the Constitution cannot be overridden by presidential action — they can be changed or undone only by overwhelming majorities in Congress or the states, with a two-thirds vote of both houses of Congress or through a constitutional convention called for by two-thirds of state legislatures.

Some conservatives have long made the argument that the 14th Amendment was meant to apply only to citizens and legal permanent residents, not immigrants who are present in the country without authorization. In an opinion piece in The Washington Post this year, Michael Anton, a former spokesman for Mr. Trump’s National Security Council, said birthright citizenship was based on a misreading of the amendment, and of an 1898 Supreme Court ruling that he argued pertained only to the children of legal residents.

“The notion that simply being born within the geographical limits of the United States automatically confers U.S. citizenship is an absurdity — historically, constitutionally, philosophically and practically,” Mr. Anton wrote in July. “An executive order could specify to federal agencies that the children of noncitizens are not citizens.”

Mr. Trump told Axios that while he initially believed he needed a constitutional amendment or action by Congress to make the change, the White House Counsel’s Office has advised him otherwise.

“Now they’re saying I can do it just with an executive order,” Mr. Trump said. The White House did not immediately respond to requests for clarification of the legal grounds the president’s lawyers have given him for validating such a move.

His discussion of the idea comes after the administration announced it was streaming more than 5,000 active-duty troops to the southern border, part of an election-season rash of executive action Mr. Trump has undertaken as he works to energize his anti-immigrant base.