President Trump Donald John TrumpOmar fires back at Trump over rally remarks: 'This is my country' Pelosi: Trump hurrying to fill SCOTUS seat so he can repeal ObamaCare Trump mocks Biden appearance, mask use ahead of first debate MORE said Tuesday he is not looking to resume the controversial practice of separating migrant children from their families at the southern border, amid bipartisan pushback against his plans to impose even stricter immigration policies.

But Trump also defended his "zero tolerance" policy as an effective deterrent, and his administration teased a raft of new, hard-line proposals intended to stem the flow of Central American migrants crossing into the U.S.

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"We're not looking to do that. No," Trump said when asked about restarting family separations during an Oval Office meeting with the Egyptian president.

The president also argued that "once you don’t have it, that’s why you see many more people coming," adding that "they're coming like it's a picnic because 'let's go to Disneyland.'"

The possibility of restoring one of Trump’s most criticized immigration policies reportedly helped trigger the exit of Homeland Security Secretary Kirstjen Nielsen Kirstjen Michele NielsenDHS IG won't investigate after watchdog said Wolf, Cuccinelli appointments violated law Appeals court sides with Trump over drawdown of immigrant protections Democrats smell blood with new DHS whistleblower complaint MORE, who once vocally supported the plan but objected to its return.

Other officials at the Department of Homeland Security (DHS) are seen as at risk of losing their jobs in a major staff shake-up engineered by White House adviser Stephen Miller and others to ease Trump’s frustration with the spike in migrant families and unaccompanied minors crossing the border.

Trump disputed the notion he is "cleaning house" at DHS, a sprawling agency tasked with overseeing immigration enforcement, cybersecurity, emergency management and more. Instead, he blamed congressional Democrats and court rulings for impeding his immigration agenda.

"We have a lot of great people over there," Trump told reporters. "We have bad laws. We have a judge that just ruled, incredibly, that he doesn’t want people staying in Mexico. Figure that one out."

Trump also blamed former President Obama for child separations, even though they were the result of the zero tolerance policy Trump enacted in April 2018 and ended last summer amid an outcry.

Multiple media outlets reported Trump had privately urged Nielsen and other officials for months to resume family separations, which sparked alarm on Capitol Hill.

"I would be completely opposed to that," Senate Homeland Security and Governmental Affairs Committee Chairman Ron Johnson Ronald (Ron) Harold Johnson CIA found Putin 'probably directing' campaign against Biden: report This week: Supreme Court fight over Ginsburg's seat upends Congress's agenda GOP set to release controversial Biden report MORE (R-Wis.) said during an immigration hearing, citing humanitarian concerns raised by a top Department of Health and Human Services official.

"I’m hoping members of the administration if they’re actually considering this are listening to that testimony," Johnson said.

Absent the policy’s return, the administration is weighing new rules and regulations designed to discourage migrant families from coming to the U.S.

A senior administration official who spoke to reporters on condition of anonymity said there are plans to draft a new regulation designed to challenge a settlement agreement stating that children cannot be held in immigration custody for longer than 20 days.

The official predicted the measure would be struck down by a federal judge but said it would be intended to spark a legal fight that reaches the Supreme Court.

Also under consideration is a "binary choice" policy that would allow migrant families to waive their rights under the agreement and remain together in detention while their cases are processed or have the adults remain in custody while their children are released after the 20-day limit.

The administration is also considering making it tougher for migrants to seek asylum, imposing stricter standards for certain immigrants to receive welfare benefits and curbing remittance payments that migrants send back to their home countries, the official said.

The potential policy shift comes as Trump and his allies have approached the situation at the southern border with a heightened sense of urgency.

U.S. Customs and Border Protection (CBP) announced Tuesday that agents apprehended more than 92,000 individuals in March trying to cross the southern border, the highest monthly tally this year and more than double the number of apprehensions reported in March 2018.

Several administration policies intended to address the situation have been blocked by federal courts, most recently its effort to keep asylum-seekers in Mexico while their cases are considered.

Vice President Pence will travel to Arizona on Thursday to meet with CBP officials and tour parts of a wall near the city of Nogales, less than a week after Trump visited a renovated section of border fencing in Calexico, Calif.

The senior administration official argued the root of the problem was a large, entrenched bureaucracy at DHS that Trump’s political appointees failed to manage. Of particular concern are career employees whom the official accused of resisting Trump’s immigration agenda.

Changing the culture, the official said, "can best be dealt with through management issues."

Trump last Friday rescinded the nomination of Ronald Vitiello to lead Immigration and Customs Enforcement. He has yet to put forward a new nominee but said he wants to go in a "tougher direction." U.S. Citizenship and Immigration Services Director Lee Francis Cissna and the department’s legal counsel are also said to be in the White House’s crosshairs.

The president said on Tuesday that his choice to lead DHS on an acting basis, CBP Commissioner Kevin McAleenan, "is going to do a fantastic job."

"We want homeland security, and that’s what we're going to get," Trump said.

McAleenan has the "full, complete and total support" of the White House "to build a team and have a fresh start to get this done," according to the official, who added that may or may not include further staff changes.

Groups advocating lower levels of immigration urged Trump to nominate former Kansas Secretary of State Kris Kobach to permanently fill the position, even though Kobach would face a difficult confirmation battle in the Senate.

"Kris Kobach is, without question, the best choice to lead DHS, and we hope he will be President Trump’s nominee," the group NumbersUSA said in a statement.

But several lawmakers, including a number of Republican senators, have taken issue with the rapid turnover atop DHS.

Sen. Mitt Romney Willard (Mitt) Mitt RomneySenate GOP aims to confirm Trump court pick by Oct. 29: report The Hill's Campaign Report: GOP set to ask SCOTUS to limit mail-in voting Senate GOP sees early Supreme Court vote as political booster shot MORE (R-Utah) said Tuesday he was "deeply troubled" by the mounting vacancies, calling it "dangerous" given the influx of migrants at the southern border and the agency’s broad scope.

Sen. Chuck Grassley Charles (Chuck) Ernest GrassleyCollins says she will vote 'no' on Supreme Court nominee before election The Hill's Morning Report - Sponsored by Facebook - Trump, GOP allies prepare for SCOTUS nomination this week Gardner signals support for taking up Supreme Court nominee this year MORE (R-Iowa) urged the president to abstain from making further changes at the agency. He specifically cautioned Trump against getting rid of Cissna, who previously worked for the Iowa Republican on the Senate Judiciary Committee, even making his case by phone to acting White House chief of staff Mick Mulvaney Mick MulvaneyMick Mulvaney to start hedge fund Fauci says positive White House task force reports don't always match what he hears on the ground Bottom line MORE.

"I know Cissna well," Grassley said, calling his former aide "good for the president."

"I heard that they were going to be dismissed, and that irritates me," he added.

Jordain Carney contributed.