Two federal judges have already put a nationwide restraining order on the ban, which restricts travel to the US from six Muslim-majority countries.
The President's new order was designed to withstand legal challenges after the first one was blocked in the courts.
Dubbing the latest legal rulings as a “terrible ruling”, Mr Trump told supporters at a campaign-style rally in Tennessee it was “a watered-down version of the first one”.
He said: “I think we ought to go back to the first one and go all the way (to the Supreme Court), which is what I wanted to do in the first place."
Norman Eisen, who worked under President Barack Obama, branded the comments a “legal disaster”, adding: “He is digging a grave for the second executive order and maybe even the third one”.
Stephen Miller, a senior adviser to Mr Trump and the architect of the first travel ban, made similar comments in January.
“Fundamentally, you’re still going to have the same basic policy outcome for the country”, Mr Miller said at the time.
This was subsequently cited as justification for the restraining order by Derrick Watson, a US district judge in Hawaii.
Judge Watson concluded that while the order did not mention Islam by name, “a reasonable, objective observer… would conclude that the executive order was issued with a purpose to disfavour a particular religion”.
A second judge in Maryland identified similar concerns, ruling that the purpose of the ban was to discriminate against Muslims.
The new executive order has removed any reference to religion and does now not involve green card holders. It also removed Iraq from the list of targeted countries.
But lawyers for the American Civil Liberties Union echoed Judge Watson’s comments, saying Mr Trump’s statements on the campaign trail, and interviews given by advisers make clear that it was an attempt to block Muslims from entering the country.
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