Still, he and Mr. Cuccinelli acknowledged that the government’s resources had been strained by the surge of migrants seeking asylum at the southwestern border.

“It’s an extraordinarily challenging situation,” Mr. McAleenan said. “I’m not denying that there are challenging situations at the border.”

Speaking to reporters, Mr. Trump called the report about the Clint facility a “hoax.”

“The Fake News Media, in particular the Failing @nytimes, is writing phony and exaggerated accounts of the Border Detention Centers,” he wrote on Twitter. “First of all, people should not be entering our Country illegally, only for us to then have to care for them. We should be allowed to focus on United States Citizens first. Border Patrol, and others in Law Enforcement, have been doing a great job.”

The Times said in a statement that it stood by the article. “We are confident in the accuracy of our reporting on the U.S. Border Patrol’s detention centers,” the statement said.

With Congress set to return on Monday after a weeklong recess for the Fourth of July holiday, lawmakers are preparing to confront the accounts of squalor in the border facilities and reports of current and former Border Patrol agents deriding migrants and making vulgar remarks about Democratic lawmakers in a private Facebook group.