President Donald Trump tweeted Sunday morning that the U.S. “Cannot accept all of the people trying to break into our Country” and called for migrants to be "immediately" deported without a trial.

“When somebody comes in, we must immediately, with no Judges or Court Cases, bring them back from where they came,” he said. His tweet did not mention people coming to the U.S. to seek asylum, which is legal to do.

"Our system is a mockery to good immigration policy and Law and Order," he said, adding in another tweet that legal entry to the country should be based on “merit.”

Immigration advocates pushed back on the comments. “What President Trump has suggested here is both illegal and unconstitutional. Any official who has sworn an oath to uphold the Constitution and laws should disavow it unequivocally,” said Omar Jadwat, director of the American Civil Liberties Union’s Immigrants’ Rights Project.

Late Saturday night, the Trump administration released a “fact sheet” noting more than 2,000 children have yet to be reunited with their parents and revealing some details about the reunification process.

The departments of Homeland Security (DHS) and Health and Human Services (HHS) said that as of June 20, 2,053 separated children remained in HHS custody, waiting to be reunited with their families as a result of the administration’s “zero tolerance” policy seeking to criminally prosecute all adults crossing the border illegally, leading to family separations.

The statement comes three days after Trump ended his policy that led to family separations, allowing families to be held together in detention centers, after an outpouring of protests.

The fact sheet released Saturday stated that the government had a “well coordinated” process of reuniting families “for the purposes of removal” — in contrast to criticism from attorneys and activists that the executive order ending family separations was creating confusion among agencies and the courts.

The statement added that children are given the opportunity to communicate with a “vetted” parent or relative within 24 hours of arriving at an HHS-funded facility, but advocates and an organization providing foster care for separated children have told NBC News it can take weeks for parents to be tracked down and able to communicate with their children by phone.

The fact sheet did not say how long the reunification process would take or whether families would be reunited while the parents' immigration proceedings were ongoing or only once they were subject for deportation. It also did not state if the process is different for families going through the asylum process.

Separately, Customs and Border Protection has reunited 522 children who were separated from their families as part of the "zero tolerance" policy.

The statement said a “small number of children” that were separated for reasons other than zero tolerance will remain separated, listing general reasons for that being if the familial relationship cannot be confirmed, if the adult is believed to be a threat to the child or if the adult is a “criminal.”

Migrants are first detained in CBP custody when they are apprehended at the border. The separated families were then split into different agencies, with adults sent to the custody of Immigration and Customs Enforcement (ICE) and the children sent to HHS custody.

The Port Isabel Service Processing Center in Texas is serving as the primary family reunification and removal center for adults in ICE custody, according to the fact sheet.

Meanwhile, another wave of protests against Trump’s immigration policies was planned in several cities nationwide on Sunday, following rallies from San Diego to New York that drew thousands on Saturday.