But after the ban was blocked and an appeals court refused to reinstate it, Mr. Trump’s lawyers slowed down the legal fight, asking for more than a month to draft a second version of the ban rather than continue to fight over the first one.

When Mr. Trump’s second attempt at a travel ban — no longer covering Iraq and deleting references to religion — was blocked by federal judges, the government asked for another month to draft its legal arguments. And this month, the Justice Department urged the Supreme Court to take up the case — not on an expedited basis, but four or five months from now, as part of the court’s regular calendar in the fall.

“The manner in which they have been pursuing the legal case undercuts the argument for the urgency of the executive order,” said Anthony Romero, the executive director of the American Civil Liberties Union, which sued over the travel bans.

But as the rules for admitting people from the six countries covered by the latest travel ban have remained almost entirely unchanged, officials have blamed a ruling by a federal judge who, in blocking the revised order, also prohibited the government from evaluating the risks of letting people enter from the affected countries.

In a legal brief on March 17, government lawyers asked the judge, Derrick K. Watson of United States District Court for the District of Hawaii, if he had meant to stop them from proceeding with the vetting review. In a reply two days later, the judge said yes.

“I can tell you right now that because of the injunction that I am not fully confident we are doing all that we can to weed out potential wrongdoers from these locations,” John F. Kelly, the Homeland Security secretary, told lawmakers during a hearing on Tuesday.

“Bottom line,” Mr. Kelly said, “I have been enjoined from doing these things that I know would make America safe.”