Administration officials privately conceded that the initial version of the order was a political debacle that damaged Mr. Trump’s nascent presidency. But they were much more sanguine about the second order, arguing that the new, multiagency review process could be used in the future to bend Mr. Trump’s uncompromising messages toward Washington’s bureaucratic realities.

Mr. Trump signed the first ban with great fanfare, in front of reporters, at the Pentagon. “We don’t want them here,” Mr. Trump said of Islamist terrorists. “We want to ensure that we are not admitting into our country the very threats our soldiers are fighting overseas. We only want to admit those into our country who will support our country, and love deeply our people.”

This time, the White House issued a photograph of the president signing the order alone at his desk in the Oval Office.

Justice Department lawyers said the revisions rendered moot legal cases against the original travel ban. But opponents said the removal of a section that had granted preferential treatment to victims of religious persecution was a cosmetic change that did nothing to alter the order’s prejudicial purpose. Immigrant rights lawyers had argued that the provision was intended to discriminate against Muslims, pointing to recent statements by Mr. Trump.

“This is a retreat, but let’s be clear — it’s just another run at a Muslim ban,” said Omar Jadwat, the director of the Immigrants’ Rights Project at the American Civil Liberties Union, one of the groups that sued to stop the first order. “They can’t unring the bell.”