"A lot of people are coming in because they want to take advantage of DACA," he added.
Former US President Barack Obama created the Deferred Action for Childhood Arrivals programme to provide temporary protection and work permits to hundreds of thousands of immigrants who are living in the US illegally after being brought here as children. Trump ended the programme last year, but gave Congress six months to pass legislation enshrining it. A deal has so far proved elusive and Trump has blamed Democrats.
It was not immediately clear what Trump was referring to when he said people are coming to take advantage of the programme.
The Department of Homeland Security is not issuing new permits, though existing ones can be renewed. The Obama administration allowed sign-ups during a set period of time, and the programme is closed to new entrants.
Proposed DACA deals crafted by lawmakers and rejected by Trump also were not open to new participants.
Trump did not explain what he meant when questioned by reporters as he entered the Church of Bethesda-by-the-Sea with the first lady and his daughter Tiffany. The White House did not immediately respond to a request for clarification.
Trump, when addressing reporters briefly before entering the church, again blamed Democrats for failing to protect the "Dreamers".
"They had a great chance. The Democrats blew it. They had a great, great chance, but we'll have to take a look because Mexico has got to help us at the border. They flow right through Mexico. They send them into the United States. It can't happen that way anymore."
Trump promised during the 2016 presidential campaign to build a southern border wall to stop illegal immigration and drugs from Mexico, but Congress has frustrated him by not moving as quickly as he wants to provide money for construction.
The president also complained on Twitter that border patrol agents can't do their jobs properly because of "ridiculous liberal (Democrat) laws" that allow people caught for being in the country illegally to be released while they await a hearing before a federal immigration judge.
Trump tweeted that the situation is "Getting more dangerous" and "Caravans" are coming. He did not offer details to back his comment.
The president's tweets came after Fox News' Fox & Friends reported early Sunday on what it said is a group of 1200 immigrants, mostly from Honduras, headed to the US. The segment was a follow-up to a report by Buzzfeed News on hundreds of Central Americans making their way through Mexico in hopes that American authorities will grant them asylum or be absent when they attempt to cross the border.
The Fox headline was "Caravan of illegal immigrants headed to US". The president is known to watch the cable TV programme in the morning.
Brandon Judd, leader of the union representing border patrol agents, predicted on Fox & Friends that those in the caravan would create havoc and chaos in the US as they wait for what he described as immigration reform. Judd also said Congress needs to pass tougher laws, an idea Trump appeared to echo, and create more bed space for immigration authorities to house people.
Some fellow Republicans chided Trump over the tone of the tweets.
"A true leader preserves & offers hope, doesn't take hope from innocent children who call America home. Remember, today is Easter Sunday," tweeted Ohio Governor John Kasich, a Trump critic who challenged him for the 2016 Republican presidential nomination.
Sunday's church visit was Trump's first public appearance with his wife since CBS's 60 Minutes aired an interview the previous Sunday with Stormy Daniels, the adult film star who says she had sex with Trump in 2006, early in his marriage and a few months after Melania Trump had given birth to their son. The White House says Trump denies the affair. Mrs Trump spent most of the past week in Palm Beach with her son.
The Trumps were returning to Washington later Sunday.
- AP
