While Thanksgiving normally signals the start of what is known as the Giving Season, President Trump didn’t appear to be in a giving mood when it comes to immigration.

Speaking to reporters while in Florida for the holiday, Trump threatened 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.

Trump also said he has given the thousands of active-duty troops he sent to the border before the Nov. 6 midterm elections the "OK" to use lethal force against migrants "if they have to." And he said Homeland Security Secretary Kirstjen Nielsen, whom he has faulted for not being tough enough on immigration, is "in there trying."

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

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"The caravans will not be permitted to enter the United States," Secretary of State Mike Pompeo said Thursday. "There are real dangers to the safety and human rights of migrants from those who would prey on them."

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.

Trump repeated Nielsen's claim, made earlier this week when she visited a San Diego Pacific Coast beach to see newly installed razor wire wrapped around a towering border wall that cuts across the sand, that there were as many as 500 criminals and gang members in the group heading northward. Nielsen refused to answer questions about how they were identified or what crimes they had committed.

Trump asserted that there are "fistfights all over the streets" in Tijuana, Mexico, and that "these are not like normal, innocent people."

"These are people you talk to them and they start a fistfight," he said. "I don't want that in this country."

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The people of Tijuana "opened up with wide arms" to welcome the caravan, Trump said, and "now they're going crazy to get them out ... because bad things are happening."

In the past week, city officials have arrested three dozen caravan members for drug possession, public intoxication, disturbing the peace and resisting police, and said they would be deported to their home countries. Many also say the actions of a few are tarnishing the image of the roughly 4,000 migrants who are camped in Tijuana.

While authorizing the military's use of lethal force along the border, Trump said, "I hope they don't have to," adding that he would not let "the military be taken advantage of. I have no choice."

Defense Secretary Jim Mattis said Wednesday that the White House had given him explicit authority to use military troops to protect Customs and Border Protection personnel at the southwest border, with lethal force if necessary. But he was adamant the military would remain within its legal limits.

The law prohibits the federal government from using the armed forces in a domestic police role, except in cases and under circumstances authorized explicitly by the Constitution or Congress. Generally, U.S. troops are authorized to use force in self-defense.

Trump said that if U.S. officials "find that it's uncontrollable, if we find that it gets to a level where we are going to lose control or where people are going to start getting hurt, we will close entry into the country for a period of time until we can get it under control. The whole border."

In that case, Mexico would take an economic hit, he said, citing an inability to ship cars into the U.S. for sale.

"We're either going to have a border or we're not," Trump said.

The Associated Press contributed to this report.