Washington — The acting head of Immigration and Custom Enforcement (ICE) on Wednesday confirmed his agency is preparing for a new wave of roundups to apprehend and deport families with open orders of removal — an operation he said will send a "powerful message" of deterrence to people in Central America considering journeying north.

Unlike President Trump — who on Monday night announced authorities would begin to deport "millions" of undocumented immigrants next week — acting ICE director Mark Morgan did not provide a time frame or concrete scope for the operation on a call with reporters. He signaled that his agency, which handles immigration enforcement in the interior of the country, will ramp up efforts to find and remove people who were placed in an expedited docket in the immigration court system but failed to report for their hearing.

The ICE chief stressed that his agency wants to uphold the values of "humanity, compassion and dignity" but that it was also critical to prevent what he portrayed as the erosion of the rule of law. "If you're here illegally, then you should be removed," Morgan said Wednesday.

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"I don't want to send ICE agents to their workplace, I don't want to send ICE agents to their homes. I don't want to send ICE agents to try to track them down and apprehend them in their communities, in their towns," he added. "That's not what I prefer to do. But we have applied due process. And we've tried to work with them. We've tried and attempted to say, 'Hey, come turn yourself in.' But they have refused to do so. So we have no choice but to carry out our statutory mandated job."

Echoing a "self-deportation" proposal floated by then-Republican candidate Mitt Romney in 2012, Morgan advised undocumented immigrants to contact their local ICE office, get their family together and "work with" the agency to deport them.

The president claimed on Monday that "millions" would be deported under a new wave of operations — something likely to be logistically impossible given the resources and manpower ICE has at its disposal. Last year, ICE removed more than 250,000 people. The highest number of yearly deportations came during the Obama administration in 2012, when the agency removed approximately 410,000 immigrants.

Any large-scale deportation blitz would also likely spark massive public outcry and affect not only undocumented immigrants with pending removal orders, but millions of mixed-status families with members who are U.S. citizens. A senior administration official told CBS News that the White House estimates that more than 1 million of the approximately 10.5 million undocumented immigrants in the country have pending removal orders.

Morgan, however, appeared to limit the group of the people who would be targeted by the expected roundups. He said the undocumented immigrants his agency will focus on were ordered deported by a judge for failing to appear in court and were also notified by ICE so the agency could organize their removal.

Morgan also mentioned that about 95% of the migrants who crossed the southern border in 2017 and were allowed into the interior have not been removed, suggesting they will be among those targeted for these operations.

Mr. Trump's bombastic vow earlier this week drew sharp criticism from immigrant advocates and Democrats, who accused him of trying to galvanize his base through anti-immigrant rhetoric and the threat of mass deportations.

"These latest comments are yet another escalation of horrific rhetoric to scare and intimidate our community for political gain," Natalia Aristizabal, an organizer for the pro-immigrant rights group, Make the Road New York, told CBS News. "As we continue to educate our loved ones and neighbors about their rights and how to stay safe, we are not confused: this is a campaign tactic to drum up support from a white nationalist base."