WASHINGTON — The Trump administration plans to aggressively push for tougher screening of asylum seekers that will make it vastly more difficult for migrants fleeing persecution in their home countries to win protection in the United States, a senior administration official told reporters on Tuesday.

The official said that President Trump ordered a shake-up of his top immigration officials in recent days because they were moving too slowly, or even actively obstructing, the president’s desire to confront the surge of migrants at the southwestern border. The asylum changes are among many policies the president wants to put into effect with a new team in place, the official said.

Mr. Trump denied on Tuesday that one of those changes would be to restart his policy of separating migrant families at the border, though he said that the act of taking children from their parents — which drew global condemnation before he abandoned it last summer — was effective.

“Now I’ll tell you something, once you don’t have it, that’s why you see many more people coming,” Mr. Trump said. “They are coming like it’s a picnic, because, ‘Let’s go to Disneyland.’”