Trump's action, announced by Attorney General Jeff Sessions on Tuesday, rescinds a programme called Deferred Action for Childhood Arrivals (DACA) which helped almost 800,000 young men and women get a legal status, work permits and driving licences.
The temporary reprieve was created by Democratic former President Barack Obama in 2012 and is supported by Democrats and many business leaders.
The Trump administration said no current beneficiaries of the programme would be affected before March 5.
Sessions said the action does not mean the DACA recipients are "bad people".
"To have a lawful system of immigration that serves the national interest, we cannot admit everyone who would like to come here. It's just that simple. That would be an open-border policy and the American people have rightly rejected that," Sessions said.
He said the programme "denied jobs to hundreds of thousands of Americans by allowing those same illegal aliens to take those jobs".
The move marked the latest action by Trump that is sure to alienate Hispanic Americans, a growing segment of the US population and an increasingly important voting bloc.
Most of the immigrants protected by DACA, dubbed "Dreamers", came from Mexico and other Latin American countries.
Jackie Cortes, a DACA recipient who came to the United States from Mexico at the age of nine, told Al Jazeera the programme helped her attend secondary school and allowed her to work "the proper way".
"I'm able to feel a part of the place that lived for more than half of my life," said Cortes.
|Sessions said no current beneficiaries of the programme would be affected before March 5 [Alex Wong/Getty Images/AFP]|
Al Jazeera's Kristen Saloomey, reporting from a pro-DACA protest outside the Trump Tower in New York, said that "people are very worried, but what is striking is that they are not staying in the shadows.
"They came here today to protest and it's been very chaotic in the last hour: dozens of demonstrators took over the Fifth Avenue and blocked traffic, with at least 11 people being arrested".
Saloomey said many of those who had been arrested were DACA recipients themselves.
"So they are putting themselves out there," she said, "willing to take a stand against this policy."
Violeta Gomez-Uribe, a DACA recipient and organiser, who came with her family to the US from Mexico more than 20 years ago, said that the policy announcement did not come as a surprise.
"This is something that we expected - it was something that was told to US since Trump was campaigning [for president]," she told Al Jazeera in New York.
"We are going to keep fighting for what we think is best for everybody - not only for the 'Dreamers', but also for the whole undocumented community that is about 11 million people."
Trump's action, deferring the actual end of the programme, effectively kicks responsibility for the fate of the Dreamers to his fellow Republicans who control Congress. But Congress has been unable since the president took office in January to pass any major legislation and has been bitterly divided over immigration in the past.
Obama bypassed Congress and created DACA through an executive order.
"The legislative branch, not the executive branch, writes these laws - this is the bedrock of our Constitutional system, which I took a solemn oath to preserve, protect, and defend," Trump said in a statement after Sessions' announcement.
"In referencing the idea of creating new immigration rules unilaterally, President Obama admitted that 'I can't just do these things by myself" - and yet that is exactly what he did, making an end-run around Congress and violating the core tenets that sustain our Republic."
Late on Tuesday, Trump said on Twitter that he would "revisit this issue" if Congress fails to "legalise DACA" in six months."
Al Jazeera's Kimberly Halkett, reporting from the White House, said that Republicans were applauding the policy announcement, but now "the problem is squarely on the lap" amid calls from organisations such as the Chamber of Commerce for a quick fix to lessen the effect on the economy.
Halkett noted, however, that this is going to be a big challenge, given the fact that many Democrats are very critical of the Trump administration's move.
"In fact, top Democrats on Capitol Hill are saying that 'this is going to have a human and economic toll' and called it 'a heartless decision that is going to rip families apart without any thought to the human consequences'."
Earlier on Tuesday, Trump had appeared determined to pressure US legislators to act. "Congress, get ready to do your job - DACA!" the president wrote on Twitter before the policy announcement was made.
There were some signs that Congress might be willing to act, with a number of senior Republican legislators coming forward to express an interest in protecting the Dreamers.
The president's decision may have been forced by nine Republican state attorneys general, led by Texas, who had threatened a legal challenge in federal court if Trump did not act to end DACA.
A number of Democratic state attorneys general have threatened legal action to defend the programme.
Source: Al Jazeera and news agencies