Eradicating “radical Islamic terrorism” from the face of the earth has been President Trump’s mantra, first in the campaign, then in his Inaugural Address and remarks a day later to the C.I.A.

No one would argue with fighting back against the Islamic State, also known as ISIS, and other terrorist groups that threaten the United States, Europe, the Middle East and beyond. For eight years, President Barack Obama did just that, using a multilayered approach that included launching thousands of air and drone strikes in at least a half dozen countries and killing countless militants, among them Osama bin Laden. While Mr. Obama made significant progress in degrading this threat — the Islamic State has lost considerable territory in both Iraq and Syria — he did not put an end to violent extremism. Mr. Trump is now pledging to do more and better.

The problem is that his approach, as we know it, is more likely to further inflame anti-American sentiment around the world than to make the United States safer. Mr. Trump has not explained how he would destroy the terrorist danger. But his use of slogans like “radical Islam,” which echo the views of his closest advisers, implies a naïve reading of the threat from about 40,000 extremists, while demonizing and alienating many of the world’s 1.6 billion Muslims.

Mr. Trump’s Plans

The emerging details suggest that Mr. Trump’s plans to eradicate violent extremists are not only at odds with Mr. Obama’s; they trample on American values and international law. It was reported on Wednesday that Mr. Trump was planning to block Syrians and others from “terror prone” nations from entering the United States, at least temporarily, even though Washington already vets visitors from such countries. While people from Syria, Iran, Sudan, Libya, Somalia, Yemen and Iraq would be blocked by a monthlong ban, Mr. Trump appears, inexplicably, to be exempting Afghanistan and Saudi Arabia, home of 15 of the 19 extremists who hijacked the planes on Sept. 11. Refugee admissions would be halted for 120 days while screening procedures are reviewed, with the number allowed in cut from 110,000 to 50,000.