Trump maintains that there are "a lot of other options", one of which is "just filing a brand new order" that might have an easier time if examined by the courts.
The ruling represented a setback for Trump's administration and the second legal defeat for the new president in the past week.
Opponents of the travel ban, led by Washington state and Minnesota and including almost 20 other states, former national security officials and leading technology companies, say the ban discriminates against citizens of certain countries and the Muslim religion.
The ban, announced January 27, temporarily barred citizens of Iraq, Iran, Libya, Somalia, Sudan and Yemen for 90 days, all refugees for 120 days, and Syrian citizens indefinitely.
They added that the government did not show evidence that any person from the affected countries had perpetrated a terrorist attack in the United States.
White House counsel Donald McGahn had issued guidance days after the executive order saying it did not apply to legal permanent residents of the U.S., but the appeals court said that was not enough.
Asked if such an order would be forthcoming, the president said: "It very well could be". Justice Department lawyers could be called upon to answer for Trump's words as the travel ban case makes it way through the courts.
August Flentje, special counsel to the assistant attorney general, argued that the president has the lawful authority to protect the national security of the country, and thus the ban should not be reviewable in court.
That court initially refused to lift Robart's restraining order on Saturday, required both sides to submit legal arguments by Monday, and held an extraordinary, hour-long telephone hearing Tuesday that was live-streamed to listeners around the world.
"T$3 he government has taken the position that the president's decisions about immigration policy, particularly when motivated by national security concerns, are unreviewable, even if those actions potentially contravene constitutional rights and protections". But it did not shy away from the larger constitutional questions raised by the order.
An official tells CNN that administration officials were not happy with the DOJ lawyer's performance during the oral arguments before the three-judge panel of the 9th Circuit and thought he was not as prepared as he should have been for the arguments against Washington and Minnesota, the states that challenged Trump's executive order.
"We had students and faculty at our state universities who were stranded overseas, we had families that were separated", Purcell said.
The controversial executive order has caused protests across America and has also led to an online petition in the United Kingdom to stop Trump's state visit to Britain later this year. The president claimed Yates had determined that the executive order was indefensible for political reasons, arguing that "Ms. Yates is an Obama Administration appointee who is weak on borders and very weak on illegal immigration".
"We therefore conclude that the states have alleged harms to their proprietary interests traceable to the executive order".
Because the ban was lifted by a judge, many very bad and risky people may be pouring into our country. A federal judge in Seattle last week issued a temporary restraining order, which put the ban on ice.
The blog post found it "remarkable" that the appellate panel "did not even bother to cite" a key USA legal statute that authorizes the president to suspend entry to the United States of all or any class of aliens he deems detrimental to U.S. interests.