Senior administration officials told CNN’s Jake Tapper that in the last four months or so, the President had been pushing then-Department of Homeland Security Secretary Kirstjen 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 public relations disaster.”He just wants to separate families,” said a senior administration official.Trump repeatedly denied that was the case on Tuesday. “We’re not looking to do that, no. We’re not looking to do that,” Trump said. But, he added, “when you don’t do it, it brings a lot more people to the border.””Now, I’ll tell you something, once you don’t have it, that’s why you have many more people coming. They are coming like it’s a picnic, like ‘let’s go to Disneyland,’ ” Trump said.He also blamed the policy on the Obama administration.”President Obama separated children. I was the one who that changed it,” he claimed.But that’s not exactly the case.The main difference between Trump and Obama, experts have said, centers on how they handled immigrants caught near the US-Mexico border. Under President Barack Obama, the Justice Department was given broad discretion on who should face criminal charges, and federal prosecutors rarely went after families.But in April 2018, then-Attorney General Jeff Sessions announced that the Justice Department would prosecute 100% of illegal border-crossers in a policy known as “zero-tolerance.” Adults went to jails and awaited criminal proceedings. Children were sent to detention centers run by the Department of Health and Human Services, and some were eventually placed in foster care.This specific change is what led to the widespread separation of parents and children, according to Jessica Bolter, a researcher with the nonpartisan Migration Policy Institute who has published 200 pages of reports on Trump’s immigration policies.CNN’s Jim Acosta also reported Monday that Trump was considering a “binary choice” policy as an alternative to the zero-tolerance policy that resulted in family separations at the border. One official said the “binary choice” proposal puts that decision of separation in the hands of parents.CNN’s Marshall Cohen contributed to this report.