Washington (CNN) President Donald Trump on Monday night issued a vague threat to deport "millions" of undocumented immigrants next week, falling short of providing any additional details and surprising officials within his own administration.

Trump said in a pair of tweets thatthe agency will begin deporting undocumented immigrants "as fast as they come in," and called on congressional Democrats to address the "Border Crisis." It wasn't immediately clear what plan Trump was talking about.

"Not a lot of happy faces" around the Department of Homeland Security, a senior administration official told CNN, as the President essentially announced an operation before it was put into action.

Trump insisted Tuesday that top immigration officials are aware of the deportation initiative he referenced in his tweets.

"They know," Trump said when asked by CNN's Pamela Brown about immigration officials who said they were caught off guard by the tweets.

"They're going to start next week," Trump continued. "When people come in illegally, they have to go out. Everybody is seeing that."

The tweets came hours before the President is set to officially kick off his 2020 bid . He launched his 2016 campaign vowing to take a hard stance against illegal immigration by building a wall and removing undocumented immigrants from the country, but deporting millions of people, as Trump suggested Monday, requires vast resources and Immigration and Customs Enforcement, DHS' enforcement arm, is already strained by migrants crossing the border illegally.

....long before they get to our Southern Border. Guatemala is getting ready to sign a Safe-Third Agreement. The only ones who won't do anything are the Democrats in Congress. They must vote to get rid of the loopholes, and fix asylum! If so, Border Crisis will end quickly! — Donald J. Trump (@realDonaldTrump) June 18, 2019

The senior administration official said the department is in the planning phase for an operation aimed at stepping up the deportation of undocumented immigrants. The expected operation will be on a "different scale" than what the public has previously seen from the department, the official said, as it will target undocumented families. The Obama administration also targeted families in the later years.

The upcoming operation will also focus on work site enforcement as well as apprehending violent criminals who are in the country illegally, the official added. "A broad section of things," the official said. Still, the official noted the operation is "not imminent" and remains in the planning stage.

Acting Homeland Security Secretary Kevin McAleenan declined to comment to CNN on the President's tweets as he left a speaking engagement Tuesday morning.

Another senior administration official told CNN on Tuesday that more than "1 million" undocumented immigrants "have been issued final deportation orders by federal judges yet remain at large in the country" and called enforcing those judicial orders a "top priority" for ICE.

"The border crisis doesn't start and stop at the border, which is why ICE will continue to conduct interior enforcement without exemption for those who are in violation of federal immigration law," ICE said in a statement Tuesday. "This includes routine targeted enforcement operations, criminals, individuals subject to removal orders, and worksite enforcement. This is about addressing the border crisis by upholding the rule of law and maintaining the integrity of the immigration system, as created by Congress."

There are around 52,000 single adults in ICE custody overall, the majority of whom are coming from the border. But DHS is unable to deport all those who are ordered to be removed from the country, given limited resources.

ICE's new acting director, Mark Morgan, said earlier this month that agency was exploring options to arrest and deport families who have gone through their legal proceedings and have been ordered to depart the US. That operation would target migrants with a "final order of removal," Morgan said.

Morgan described the potential deportation of families as a way to reduce the incentive for migrants to travel to the United States. Families are often released into the US following their apprehension, due to limits on the time children can be held in government custody.

Former Homeland Security Secretary Kirstjen Nielsen had rejected the plan because the policy of the department was to prioritize criminals for deportation, according to one US official.

Under former President Barack Obama, the department had deployed an operation targeting families in the later years. It was revived in Trump's first year in office.

CNN first reported that the Trump administration was considering deporting migrant families with court-ordered removals. The administration had been looking at Obama-era policies such as Operation Border Guardian/Border Resolve, which targeted family units for removal amid an uptick in families and unaccompanied minors attempting to cross the border.

The increasing number of apprehensions at the southern border, and makeup of those apprehensions, has overwhelmed the Department of Homeland Security. In May, nearly 133,000 migrants were arrested for illegally crossing the border, more than 11,000 of whom were unaccompanied children, according to Customs and Border Protection data

While the administration argues deportations will stanch the flow of migrants to the border, it's unclear whether the President's tweet will upend any future operation.

Last year, the President expressed frustration toward Oakland, California, Mayor Libby Schaaf after she issued a public warning for the immigrant communities in her city about impending raids by ICE in the the San Francisco Bay Area.

"They had close to a thousand people ready to be gotten, ready to be taken off the streets ... they say 85% of them were criminals and had criminal records. And the mayor of Oakland went out and warned them all," Trump said at the time, adding that her actions were a "disgrace."