WASHINGTON — President Trump vowed on Friday to order new security measures by next week intended to stop terrorists from entering the United States, even as aides debated whether to ask the Supreme Court to reinstate his original travel ban that has now been blocked by lower courts.

A day after a three-judge panel rebuffed him, Mr. Trump said he might sign “a brand-new order” as early as Monday that would be aimed at accomplishing the same purpose but, presumably, with a stronger legal basis. While he vowed to keep fighting for the original order in court, he indicated that he would not wait for the process to play out to take action.

“We will win that battle,” he told reporters on Air Force One as he flew to Florida for a weekend golf outing with Prime Minister Shinzo Abe of Japan. Yet noting that it most likely would not happen quickly, he also raised the possibility of “a lot of other options, including just filing a brand-new order.”

Asked if he would do that, Mr. Trump said, “We need speed for reasons of security, so it very well could be.”