President Trump had said the executive order would be announced this week, but White House officials have now told reporters it is being delayed.
The original order banned refugees and immigrants from seven mostly Muslim countries from entering the US.
The order sparked mass protests and confusion at airports, and US courts have temporarily blocked the ban.
The White House has said the rewritten order will address some of the issues brought up in the courts, while Homeland Security Secretary John Kelly has said it will be a "tighter, more streamlined version of the first executive order".
It is not clear how the new text will differ from the original measure.
Commentators say a repeat of the chaos that followed the initial order could be another blow to an administration that has been at the centre of a series of controversies with just one month in office.
Mr Trump's initial order, signed in January, banned anyone from seven majority-Muslim countries - Iran, Iraq, Syria, Yemen, Somalia, Sudan and Libya - from entering the US for 90 days.
It also halted refugee resettlement for 120 days and banned Syrian refugees indefinitely.
But the measure was blocked by a Seattle court, in a decision that was later upheld by 9th US Circuit Court of Appeals, which said the government had not proved the terror threat justified reviving the ban.
Mr Trump has criticised the court decision, saying "the security of our nation is at stake".
The US government has pushed back the unveiling of a new, updated travel ban until next week.