March 30, 2017 0850 GMT
Trump made the remarks on Friday aboard Air Force One on his way to Florida, after his administration suggested it would not ask the Supreme Court to review a federal appeals court decision that keeps the travel ban frozen.
The US Court of Appeals for the Ninth Circuit in San Francisco, California, ruled on Thursday that a nationwide restraining order against the president’s travel ban may continue while a federal judge considers a lawsuit over the immigration policy.
The Trump administration can appeal to the Supreme Court to immediately intervene, or wait until a ruling on the preliminary injunction order.
But Trump told reporters on Friday, "We also have a lot of other options, including just filing a brand new order.”
Asked if he is planning to issue a new executive order, Trump said, "It very well could be. We need speed for reasons of security, so it very well could be."
He said that he might take action on Monday or Tuesday.
Earlier in the day, Trump said that he will introduce new measures as early as next week to keep the country safe against threats, indicating a new executive order is coming.
"We'll be doing something very rapidly having to do with additional security for our country," Trump said during a joint press conference with Japanese Prime Minister Shinzo Abe at the White House. "You’ll be seeing that sometime next week.”
“We’ll be going forward and we'll be doing things to continue to make our country safe,” he continued. “It will happen rapidly and we will not allow people into our country who are looking to do harm to our people.”
Trump went on to say he is totally confident that his administration will bring what he called tremendous security for the American people.
He once again warned that the US is facing serious threats and pledged to push ahead with his plans.
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Trump signed an executive order on January 27 that imposed a temporary travel ban on citizens from Iran, Iraq, Libya, Somalia, Sudan, Syria and Yemen and placed an indefinite ban on Syrian refugees. The move also suspended admission of all refugees for 120 days.
But, days after District Court Judge James Robart’s order lifted his administration's travel ban.
Robart's decision came after Washington state Attorney General Bob Ferguson filed a lawsuit to invalidate key provisions of Trump's executive order.
Robart questioned the Trump administration's use of the September 11, 2001 terror attacks on the US as a justification for the travel ban.