Mr Trump spoke to reporters on Air Force One
The White House has said there are no plans to escalate the legal fight surrounding US President Donald Trump's travel ban to the Supreme Court.
After an appeals court ruled that immigration restrictions on travellers from seven Muslim-majority countries should remain suspended, Mr Trump told reporters on Air Force One: "We also have a lot of other options."
One of those options might involve rewriting the controversial executive order, or replacing it with a new one, to sidestep the legal issues which have caused the travel ban to become held up in the courts.
The president said it is likely that "very little" would be changed in a second executive order, and hinted that it could be signed as early as Monday or Tuesday.
"We need speed for reasons of security. So it could very well be that we do that," Mr Trump added.
On Thursday, the president had responded furiously after a panel of three judges ruled that the government had not provided "any evidence" of national security concerns which had justified banning migrants, visitors and refugees from Iraq, Iran, Syria, Somalia, Yemen, Libya and Sudan.
Moments after the ruling, Mr Trump had tweeted: "SEE YOU IN COURT, THE SECURITY OF OUR NATION IS AT STAKE!"
Fighting to get the travel ban reinstated in the Supreme Court had been considered likely.
However, there are only eight justices instead of the usual nine on the bench at present - and they could have delivered a deadlocked result of 4-4 if they were asked to weigh in on the case.
This would mean the suspension would remain in force.
Instead, a senior White House official has suggested the constitutionality of the travel ban will be argued in the lower courts.