PALM BEACH, Fla. — President Trump made a Thanksgiving Day threat to close the U.S. border with Mexico for an undisclosed period of time if his administration determines that its southern ally has lost "control" on its side.

Mr. Trump, speaking to reporters after a teleconference with troops from his Mar-a-Lago resort in Florida, claimed he shut down the border in a sense a couple days ago. He wouldn't elaborate on that. He also said Homeland Security Secretary Kirstjen Nielsen, whom he has faulted for not being tough enough on immigration, is "in there trying" to manage the border crisis.

"It's a tough job," he said.

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The president would not discount the possibility of a partial government shutdown early in December over lawmakers' refusal to allocate the billions of dollars he is demanding for a border wall, the central promise of his 2016 campaign.

"Could there be a shutdown? There certainly could, and it will be about border security, of which the wall is a part," Mr. Trump said.

That conversation with troops grew from a presidential expression of gratitude for their commitment to protecting the country and its interest and touched on a variety of political topics, including immigration policy, the economy and Mr. Trump's displeasure with court rulings against administration initiatives.

Mr. Trump's border threat came days after a federal judge put the administration's asylum policy on hold. Under that new policy, Trump declared no one could apply for asylum except at an official border entry point. Some ports of entry are already facing huge backups, with people waiting for weeks.

The U.S. government shut down one port of entry, San Ysidro, in California, for several hours early Monday morning to bolster security amid concerns about a potential influx of migrant caravan members. Most of the lanes were reopened before the morning rush.

Mr. Trump's remarks come on the heels of a memo signed by White House chief of staff John Kelly declaring the Pentagon has the authority to allow troops to use force, including lethal force, to protect federal personnel at the border if necessary. The memo, dated Tuesday, says troops at the border "may perform those military protective activities that the secretary of defense determines are reasonably necessary to ensure the protection of federal personnel, including a show or use of force (including lethal force, where necessary), crowd control, temporary detention, and cursory search."

"The deployed military personnel shall not, without further direction from you, conduct traditional civilian law enforcement activities, such as arrest, search and seizure in connection with the enforcement of the laws," says the memo, which was obtained by CBS News national security correspondent David Martin.

Mr. Trump confirmed in his wide-ranging Q&A session with reporters Thursday that he has given troops the authority to use lethal force, if needed.

"If they have to they are going to use lethal force — I've given the okay, yeah," the president said. "If they have to, I hope they don't have to. But you know you are dealing with a minimum of 500 serious criminals. So I'm not going to let the military be taken advantage of, I have no choice, do I want that to happen, absolutely not, but you are dealing with rough people."

White House deputy press secretary Hogan Gidley said that the "brave men and women at Customs Border and Protection willingly put themselves in extremely dangerous situations every day to protect Americans and their families. The president's authorization ensures the Department of Defense can step in to protect those who protect us."

Mr. Trump expressed little concern earlier this week that more than 5,000 troops are spending Thanksgiving at the border.

"Oh you -- don't worry about the Thanksgiving-- these are tough people," Mr. Trump said before boarding Marine One on his way to Mar-a-Lago. "They know what they're doing and they're great. And they've done a great job You're so worried about the Thanksgiving holiday for them."