"We'll win that battle," Mr Trump told reporters, adding: "The unfortunate part is it takes time. We'll win that battle. But we also have a lot of other options, including just filing a brand new order."
A unnamed judge from the 9th US Circuit Court of Appeals, which on Thursday upheld the stay on the original order, has called on all 25 judges of that court to vote on whether to hear the appeal again.
Technically known as an en banc review, a second hearing of the case would involve an 11-judge panel, rather than the three who initially heard the appeal.
Mr Trump's travel ban, which was hastily unveiled at the end of his first week in office, caused chaos at US airports and sparked protests across the country.
On Thursday, the appeals court said the administration failed to offer "any evidence" to justify the ban, which the president said was necessary to keep the US safe from terror attacks.
However Mr Trump insisted that the executive order was crucial for national security and promised to take action "very rapidly" to introduce "additional security" steps in the wake of the court's decision.
He spoke as Virginia state lawyers argued in court that his policy "resulted from animus toward Muslims".
Their challenge focuses on the travel restrictions imposed by the ban, rather than the four-month suspension of refugee admissions.
But lawyers for the US government in Virginia wrote that "judicial second-guessing" amounted to "an impermissible intrusion" on Mr Trump's constitutional authority.
The appeals court ruling means that visa holders from Iran, Iraq, Libya, Somalia, Sudan, Syria and Yemen can continue to enter the US, and refugees from around the world, who were also subject to a temporary ban, are no longer blocked either.
But the ruling does not affect one part of Mr Trump's controversial executive order: a cap of 50,000 refugees to be admitted in the current fiscal year, down from the ceiling of 110,000 established under his predecessor, Barack Obama.