The news follows a Ninth Circuit Court of Appeals decision to uphold a temporary restraining order against Trump's temporary executive order restricting immigration and travel from seven Muslim-majority countries linked to terrorism.

On Air Force One, Trump said, "We will perhaps do that. We'll see. Monday or Tuesday."

Immigration agents have rounded up hundreds of illegal immigrants in the past few days, concentrating, The White House says, on violent criminals.

"The crackdown on illegal criminals is merely the keeping of my campaign promise," the president tweeted. "Gang members, drug dealers & others are being removed!"

As for a new executive order, Trump said, "We'll win that battle. We also have a lot of other options, including filing a brand new order. Could very well be, and I like to, I like to surprise you."

The White House says any new executive order would likely have a much narrower scope, like suspending new visas and refugees from the seven countries on Trump's list. Anyone already cleared would be allowed to keep their visas.

"There is no constitutional right for a citizen in a foreign country who has no status in America to demand entry into our country," White House Senior Policy Adviser Stephen Miller told ABC's "This Week."

"Such a right cannot exist; such a right will never exist," he insisted. "This is an ideological disagreement between those who believe we should have borders and should have controls, and those who believe there should be no borders and no controls."

Meanwhile, the president faces an international test as well. (Photo: Cabinet Public Relations Office/Handout via Reuters)

As he hosted Japanese Prime Minister Shinzo Abe at his Mar-a-Lago estate, it was confirmed that North Korea fired a ballistic missile into the Sea of Japan. The leaders called the test launch "intolerable"—with Trump saying the U.S. has Japan's back "100 percent."

But on the White House's primary issue of the moment, the administration seems determined to win the immigration battle, with Miller saying "all options are on the table."

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