He sees the issue as crucial ahead of midterm congressional elections in November.
"We cannot allow all of these people to invade our Country," Trump said yesterday on Twitter.
"When somebody comes in, we must immediately, with no Judges or Court Cases, bring them back from where they came," said Trump, suggesting they be handled without the due legal process guaranteed for "any person" by the US Constitution.
Nearly all of the arriving families have officially requested asylum.
"Our system is a mockery to good immigration policy and Law and Order," said Trump, who has repeatedly tried to link immigrants with crime.
His remarks came after the Department of Homeland Security released its first official data since Trump ended the family separations on Wednesday.
It said 522 children separated as part of "zero tolerance" have been reunited with their families, but another 2,053 separated minors remained in the care of the US Department of Health and Human Services as of Wednesday.
"The United States government knows the location of all children in its custody and is working to reunite them with their families," the department said in a statement late Saturday.
Fleeing from impoverished Central America, the arrivals say they are seeking a better life and also a refuge from criminal gangs terrorizing their region, which has one of the world's highest murder rates.
Central American migrants deported from the US without their children have spoken of their anguish at seeing families split under the "zero tolerance" approach.
Ever Sierra, deported after trying to enter the US, told AFP he planned to try again in a few days.
He arrived back in Honduras with his eight-month-old daughter's shoes hanging from his backpack. She was being held in a detention centre in McAllen, Texas, along with her mother.
Benjamin Raymundo, a 33-year-old deported back to Guatemala, told AFP he left his home country in April with his son Roberto, aged five, but the pair were separated when immigration officers in California stopped them.
The boy was eventually placed in a relative's custody.
"It's a great sadness for me, as if I'll never see my son again," Raymondo lamented.
Trump's former deputy national security advisor, Tom Bossert, said the past week had provided "terrible optics" for the administration, and "almost from the outset we didn't have the capacity to detain these parents and children, together or separately."
Speaking on ABC's "This Week," Bossert predicted that Trump's executive order ending the family separations will not stand up in court because a judge had ruled in 2015 that even detaining parents and children together is "inhumane."
US lawmakers on Sunday spoke of the need for a longer-term solution. But in a poisoned political climate, they have failed to advance either of two Republican immigration bills in the House of Representatives, which the Republicans control along with the Senate.
A hardline proposal was defeated last week, as expected, and a vote on a "compromise" bill between the party's hard-right and moderate factions has been pushed back, with signs it could not pass.
Trump and other hardline Republicans accuse opposition Democrats of being soft on crime and immigration.
On Saturday, former Republican presidential hopeful Mike Huckabee posted a picture on Twitter of MS-13 gang members and joked that the heavily tattooed Latinos were the "campaign committee" for top Democrat Nancy Pelosi.
Trump frequently brings up the Hispanic gang when he talks of immigration.
(Only the headline and picture of this report may have been reworked by the Business Standard staff; the rest of the content is auto-generated from a syndicated feed.)