President Donald Trump speaks during a meeting with Egypt's President Abdel Fattah Al Sisi in the Oval Office at the White House in Washington, April 9, 2019.

President Donald Trump on Tuesday denied reports that he wants to restart a policy of family separation at the U.S.-Mexico border.

"We're not looking to do that," Trump told reporters. But "once you don't have [family separation], that's why you have many more people coming," the president continued. "They are coming like it's a picnic, like 'let's go to Disney Land.'"

Trump also claimed the controversial policy originated with his predecessor, and not with his own administration. "President Obama separated the children," Trump claimed. "I was the one who changed that."

Trump made the remarks at a meeting in the Oval Office with Egyptian President Abdel-Fattah el-Sissi.

Official Washington was still reeling Tuesday following what were widely seen as the first steps in a purge by the president of the top leadership at the Department of Homeland Security.

Trump also denied that he is "cleaning house" at the department, saying lots of "good people" still work at DHS.

In the past five days, Trump has fired Nielsen, told Alles to resign, and withdrawn his nomination of Ron Vitiello to lead U.S. Immigration and Customs Enforcement. Trump is also reportedly considering replacements for the director of U.S. Citizenship and Immigration Services, currently held by Francis Cissna, and the Homeland Security Department's general counsel, currently occupied by John Mitnick.

In the cases of Nielsen and Vitiello, Trump has signaled that he wants someone in their positions who is more enthusiastic about implementing some of his administration's more drastic proposals to stem the growing tide of asylum-seekers arriving at the U.S.-Mexico border.

These reportedly include reimplementing the "zero-tolerance" family separation policy that Trump officially enacted in the spring of last year, but which he rescinded two months later.

The policy sparked a bipartisan outcry after first-person accounts and footage emerged of children, some as young as four, being kept in wire pens without their parents while they awaited processing.

On Monday, NBC News reported that Trump has been privately urging officials at DHS for months to return to the family separation policy.

Underlying Trump's interest in reinstating the policy is a belief, which the president alluded to on Tuesday, that separating parents and children at the border is an effective deterrent to migrant families who might decide to seek asylum in the United States.

During the past year, the U.S. has seen a surge in the number of migrants seeking asylum at the southern border, a group increasingly comprised of families with children fleeing three Central American countries plagued by corruption and gang violence: Guatemala, El Salvador and Honduras.