Trump says he's the only one in charge of setting his immigration policy

Trump avoided answering whether he's considering a new separation policy.

“Frankly, there is only one person that is running it. You know who that is? It's me,” Trump said, pointing at his head, when asked about the Department of Homeland Security and whether he would ever consider appointing Miller to lead DHS.

Even as he pushed back, the president offered warm words for Miller.

"Stephen is an excellent guy. He is a wonderful person. People don't know him. He has been with me from the beginning. He is a brilliant man,” he said of Miller.

The president’s comments come amid reports that Miller has been heavily influencing the president’s decision-making as he has executed top firings at DHS and is looking to crack down on border crossings and make it harder for migrants to apply for asylum.

The president did not directly answer a question about whether he’s weighing implementing a so-called “binary choice” policy to allow migrant parents the choice of being separated from their children or submitting to their children remaining in long-term detention with them as their appeals for asylum are being heard in a U.S. immigration court.

Trump did, however, blast the nation’s asylum rules more broadly.

“I think that the whole asylum rules, laws, and regulations have been taken advantage of by people that are very bad people in many cases. These are the people running the cartels. They are gaming the system,” Trump said.

President Trump's outgoing DHS Secretary Kirstjen Nielsen is set to formally resign Wednesday, after initially submitting her forced resignation on Sunday. The current leader of Customs and Border Protection, Kevin McAleenan, will assume the role of Acting DHS secretary at the president's request.

Trump's appointment of McAleenan resulted in another forced resignation of the department's acting deputy, Claire Grady, who was next in line to succeed Nielsen under DHS rules. The administration also announced on Monday that the head of the Secret Service would soon be departing the administration.

Trump continued railing against the nation's immigration laws later in the day during an impromptu press spray of a fundraiser in San Antonio, where he said several attendees had been telling him graphic stories about the dire situation on the southern border.

For 30 minutes, Trump and the group painted a dark portrait of the dangers of illegal immigration both for the migrants making the trip north and those in communities near the border, and why it justifies Trump’s calls for a wall.

“If we had the wall, the good people will not be able -- you'll see them on the other side of the wall,” Trump said.

Speaking of ranchers living near the border, the president said, “They're told never to leave their house at night. And during the day, always carry a gun and know how to use it.”

Referring to what one attendee told him, Trump at one point suggested that migrants from the Central American countries are “much more dangerous” than those from Mexico.

“People from, you said before, Colombia, and also, you said Guatemala, Honduras, El Salvador are much tougher people, much more dangerous people?” he asked.

At one point, one of the attendees at the table said of some of those who cross the border illegally wear all-black outfits and stand on the porches of people's houses to intimidate them.

“They've got hoodies on," the unidentified person said. "These are not good guys.”

Trump also falsely claimed that Democrats are only fighting against his border policies because they want to get votes from those who come into the country illegally.

“We're represented by Democrats who don't want to hear it, because to them, they will take anybody, they don't care about crime, they just want to get votes,” Trump said. “They think these will all be votes to them someday, and other reasons. Maybe they want to make the country look bad.”

ABC News' Alexander Mallin contributed to this report.