Speaking to reporters aboard Air Force One, Mr Trump said his administration has “a lot of options” to achieve its aim of restricting immigration from seven Muslim-majority countries.
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.
Mr Trump 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,” the President added during the surprise visit to the press cabin, where he was accompanied by First Lady Melania Trump.
Green card holders or permanent residents from the seven affected countries may be excluded from the travel ban if the decree is revised, according to a congressional aide.
A White House official had initially suggested that the Trump administration was not planning to ask the Supreme Court to overturn Thursday’s ruling by the 9th Circuit Court of Appeals in San Francisco.
But Reince Priebus, the White House’s chief of staff, later contradicted this by saying a Supreme Court fight remains a possibility – adding: “Every single court option is on the table.
“And, in addition to that, we’re pursuing executive orders right now that we expect to be enacted soon that will further protect Americans from terrorism.”
Meanwhile, a judge in the 9th Circuit Court of Appeals – which was responsible for upholding the travel ban suspension – has requested a vote on whether to hear the case again in front of a larger panel of justices.
Three judges had heard the case between the US Justice Department and the state of Washington, but an “en banc” review would involve another hearing before 11 judges.
On Thursday, the President had responded furiously after the three justices ruled that government lawyers 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 could be a challenge for the President.
There are only eight justices instead of the usual nine on the bench at present – and they could deliver a deadlocked result of 4-4 if they were asked to weigh in on the case, meaning the suspension would remain in force.
The uncertainty of where the legal battle will end is causing many citizens of the affected countries to travel to the US with urgency.
But some foreign-born US citizens who need to make trips back to one of the seven nations are having to abandon their plans – potentially creating life or death situations.
A surgeon in Texas, who was originally born in Iran, has had to cancel a journey to his home country where he was due to operate on unborn children.
Dr Alireza Shamshirsaz is one of the world’s few specialists in foetal surgery, but he has had to tell two sets of parents in Iran that he will be unable to travel there for fear of being left stranded.
“It was a disaster. They were sobbing, completely and totally devastated. Now, there is no hope for them,” Dr Shamshirsaz told the Houston Chronicle.