May 25, 2017 0413 GMT
"We will be issuing a new and very comprehensive order to protect our people," he told a news conference, AFP reported.
The Justice Department announced soon after that it wants to drop an appeal against a court ruling that suspended the travel ban targeting nationals from seven mainly Muslim countries as well as all refugees.
The January 27 order was widely criticized as amounting to simply a ban on Muslims, and also for being rolled out sloppily – with virtually no warning to the public or preparation of the agencies tasked with enforcing it.
It triggered worldwide outrage as well as protests in America and chaos in the first days of its implementation as people arriving at US airports from targeted countries were detained and sometimes sent back to where they came from.
Trump on Thursday nevertheless hailed the introduction of the travel ban as smooth. He criticized the court order suspending the ban as "a very bad decision, very bad for the safety and security of our country. The rollout was perfect".
The Justice Department announced it would drop the attempt to salvage Trump's executive order in a brief filed with the Ninth Circuit Court of Appeals in San Francisco. But it is not a given the case will be dropped. The government asked that it at least be put aside as the administration prepares its new immigration order.
The new order would address complaints from a three-judge panel of the court to the effect that parts of the first order were unconstitutional, the department said.
"Rather than continuing this litigation, the president intends in the near future to rescind the order and replace it with a new, substantially revised executive order to eliminate what the panel erroneously thought were constitutional concerns," the brief states.
"In so doing, the president will clear the way for immediately protecting the country rather than pursuing further, potentially time-consuming litigation," it added.