"Can not accept all of the people trying to break into our Country", he tweeted.
Trump said once "somebody comes in" the country, they should be removed with "no Judges or Court Cases" - a move that would violate the long-established legal precedent for immigrants' rights to due process.
It was unclear if Trump was advocating an expansion of the current law that allows expedited removal of illegal immigrants at the United States border, a policy his administration has embraced since he took office.
Wisconsin GOP Sen. Ron Johnson said Sunday the laws and practices of the USA have encouraged undocumented immigration to levels the nation can not handle.
"Here, I think he is making it clear, he just doesn't want anybody here".
Mr. Trump accused the Democrats of blocking negotiations throughout the week.
Republican leadership has struggled for years to come together on immigration and had failed in recent months to present a deal to House Republicans, opening the door for a group of moderate lawmakers to move forward with a maneuver to force a vote - over leaders' objections - on the issue.
A new CBS poll underscored the Republican dilemma on the issue.
Starbucks to accelerate store closings next year
Starbucks says it will also add more teas to its menu and plans on " capitalizing on health and wellness trends " Bloomberg notes. The chain is also relying on its digital initiatives to contribute between 1 and 2 percent to comparable sales next fiscal year.
Democrats and other opponents of the administration's policy say that court case is not the root of the problem, noting that separating families was the exception, not the rule, for most of the two decades since the Flores case was resolved. Asked if Trump was doing that, Walden pivoted toward a door and said, "I'll leave it at that".
But the controversy raging over the issue has persuaded many lawmakers they have to look like they are addressing the subject now.
GOP leaders said the House will vote on its compromise immigration bill despite Trump's flashing red light on the subject.
Trump told House Republicans last week that he was "100 percent" behind the effort but tweeted days later that they were "wasting their time" voting before the midterm elections.
Last week, Trump reversed a policy of separating families entering the USA illegally at the border with Mexico.
Instead, Republican blockades against ending deportations of young immigrants brought to the USA illegally as children were major news earlier this year. "Most children come without parents", he tweeted Sunday morning. Intense criticism of the policy caused Trump to sign an executive order last week to end the separation of families.
Despite that tweet, Trump then continued to talk about immigration in subsequent following tweets.
However, he defended his policy, pointing out former President Barack Obama had similar policies enforced when he was in office.
In a fact sheet released Saturday evening, the Department of Homeland Security said 522 children who had been separated from their families were since reunited, but provided no timeline for when the rest of the reunions would happen.