By Jake Tapper, Anchor and Chief Washington Correspondent

(CNN) -- President Donald Trump has been pushing to reinstate broader family separation policies and sought to close the US-Mexico border at El Paso, Texas, as his conflict with Homeland Security Secretary Kirstjen Nielsen reached a boiling point.

Three Thursdays ago, in a meeting at the Oval Office with top officials -- including Nielsen, Secretary of State Mike Pompeo, top aides Jared Kushner, Mercedes Schlapp and Dan Scavino, White House counsel Pat Cipollone and more -- the President, according to one attendee, was "ranting and raving, saying border security was his issue."

Senior administration officials say that Trump then ordered Nielsen and Pompeo to shut down the port of El Paso the next day, Friday, March 22, at noon. The plan was that in subsequent days the Trump administration would shut down other ports.

Nielsen told Trump that would be a bad and even dangerous idea, and that the governor of Texas, Republican Greg Abbott, has been very supportive of the President.

She proposed an alternative plan that would slow down entries at legal ports. She argued that if you close all the ports of entry all you would be doing is ending legal trade and travel, but migrants will just go between ports.

According to two people in the room, the President said: "I don't care."

Ultimately, acting White House chief of staff Mick Mulvaney seemed to have been able to talk the President out of closing the port of El Paso. Trump, however, was insistent that his administration begin taking another action -- denying asylum seekers entry. Nielsen tried to explain to the President that the asylum laws allow migrants from Central America to come to the US and gain entry. She talked to the White House counsel to see if there were any exceptions, but he told her that her reading of the law was correct.

Neither the White House nor the Department of Homeland Security responded to official requests for comment.

Told agents not to let migrants in

Last Friday, the President visited Calexico, California, where he said, "We're full, our system's full, our country's full -- can't come in! Our country is full, what can you do? We can't handle any more, our country is full. Can't come in, I'm sorry. It's very simple."

Behind the scenes, two sources told CNN, the President told border agents to not let migrants in. Tell them we don't have the capacity, he said. If judges give you trouble, say, "Sorry, judge, I can't do it. We don't have the room."

After the President left the room, agents sought further advice from their leaders, who told them they were not giving them that direction and if they did what the President said they would take on personal liability. You have to follow the law, they were told.

More widespread family separations policy

Senior administration officials also told CNN that in the last four months or so, the President has been pushing Nielsen to enforce a stricter and more widespread "zero tolerance" immigration policy -- not just the original policy started by former Attorney General Jeff Sessions and undone by the President once it was criticized -- that called for the prosecution of individuals crossing the border illegally between ports of entry, resulting in the separation of parents from children.

According to multiple sources, the President wanted families separated even if they came in at a legal port of entry and were legal asylum seekers. The President wanted families separated even if they were apprehended within the US. He thinks the separations work to deter migrants from coming.

Sources told CNN that Nielsen tried to explain they could not bring the policy back because of court challenges, and White House staffers tried to explain it would be an unmitigated PR disaster.

"He just wants to separate families," said a senior administration official.

Last night, on the second floor of the East Wing of the White House residence -- in a room called the yellow oval -- Nielsen, Mulvaney and the President met. Nielsen tried to present a path forward that was legal and in compliance with US laws but the President said to her, "This isn't working." And Nielsen did not disagree.

"At the end of the day," a senior administration official said, "the President refuses to understand that the Department of Homeland Security is constrained by the laws."

CORRECTION: This story has been updated to accurately reflect that the Oval Office meeting to discuss closing the border occurred on Thursday, March 21.