The decision also could provide more ammunition in court to challengers of the executive order.
The new executive order was slated for a mid-week release, but a senior administration official told CNN after Trump's speech to a joint address of Congress that the timeline was being pushed back in order to keep the spotlight on the positive reaction to his address.
"We want the (executive order) to have its own 'moment,'" the official said.
The open admission that the ban -- which the administration has pitched as an emergency imperative -- angered and emboldened opponents on Capitol Hill and at the American Civil Liberties Union.
"National security experts from both parties have said the ban was unnecessary. That the administration has delayed issuing a revised ban for so long, in part for political reasons, further undercuts the argument that a ban is urgently needed for security reasons," Lee Gelernt, deputy director of the ACLU's Immigrants' Rights Project, told CNN on Wednesday.
CNN has reached out to the White House for comment. But when asked Wednesday about the timing of the upcoming executive order at the White House, press secretary Sean Spicer only said: "When we have one, we'll announce it."
Rep. Adam Schiff, D-California, the ranking member of the House Intelligence Committee, was one of a number of elected officials to suggest the White House's decision had exposed political motivations.
"The fact that the President thinks, 'Well, we can wait another day so I can get a political benefit from a day focused on my speech' tells you they don't see that much urgency either," he told CNN's Kate Bolduan. "It looks arbitrary and political, which is exactly, I'm afraid, what it is."
Sen. Jeanne Shaheen, a New Hampshire Democrat, was similarly critical.
"Delaying @RealDonaldTrump's #MuslimBan for press coverage proves that his order is about politics not security," she tweeted. "Time to scrap it entirely"
By openly attributing the delay to political calculations, the administration also imperils its argument in the courtrooms where its fate will likely be decided after a new round of legal challenges are filed in response.
On February 5, with the initial order held up in court, Trump attacked a judge on Twitter, suggesting the delay could jeopardize national security.
"Just cannot believe a judge would put our country in such peril," he said. "If something happens blame him and court system. People pouring in. Bad!"
In one section of a legal brief filed by the administration, entitled, "Facts showing the existence and nature of emergency," the Justice Department argued that the district court decision blocking the ban imposes "irreparable harm" on the government and general public. "The injunction immediately harms the public," Justice Department lawyers wrote.
They added: "The President, moreover, has determined that while such review is ongoing, the potential risk of admitting nationals from certain terrorism-compromised countries, who may be bent on harming US national security, is too high."
Indeed, in one court filing, the word "risk" appeared at least 14 times.
The first executive order banned citizens from seven Muslim-majority countries from entering the US for 90 days, temporarily suspended the entry of all refugees and indefinitely closed out Syrian refugees. Its surprise implementation caused chaos and confusion at airports around the country, as travelers with various visas were detained and, in some cases, allegedly denied access to lawyers by customs agents.
During and after the rash of protests that followed, federal courts stayed or issued temporary injunctions that effectively halted the ban nationwide. The Trump administration chose not to run the case any further up the judicial ladder -- at least for now -- instead opting to rewrite the order under more exacting legal supervision.
The new ban is expected to exclude legal permanent residents and existing visa holders entirely, sources familiar with the plans told CNN.
But there is also debate within the administration
-- another potential reason for the holdup -- over whether to remove Iraq from the list, with Secretary of State Rex Tillerson, Secretary of Defense James Mattis, and national security adviser H.R. McMaster all asking that it be excluded for diplomatic reasons, including the Iraqi military's role in the ongoing campaign to flush ISIS out of Mosul.