US President Donald Trump has reasserted his opposition to legalising the status of hundreds of thousands of undocumented immigrants brought to the United States as children.
He declared on Twitter that Republicans should "go to Nuclear Option to pass tough laws [on illegal migrants] NOW".
Mr Trump also accused Mexico of doing "very little, if not NOTHING" to stop migrants flowing into the US.
The top candidates for Mexico's presidency have hit out at Mr Trump.
On Monday, he again took to Twitter to criticise US border security and immigration laws.
DACA is dead because the Democrats didn’t care or act, and now everyone wants to get onto the DACA bandwagon... No longer works. Must build Wall and secure our borders with proper Border legislation. Democrats want No Borders, hence drugs and crime!— Donald J. Trump (@realDonaldTrump) April 2, 2018
...Congress must immediately pass Border Legislation, use Nuclear Option if necessary, to stop the massive inflow of Drugs and People. Border Patrol Agents (and ICE) are GREAT, but the weak Dem laws don’t allow them to do their job. Act now Congress, our country is being stolen!— Donald J. Trump (@realDonaldTrump) April 2, 2018
Mr Trump wanted to scrap the Deferred Action for Childhood Arrivals (Daca) programme from March.
But judges halted the move, saying the Obama-era scheme providing protected status to those who entered the US illegally as children must remain in place while legal challenges are heard.
The scheme is now closed to new entrants but existing members may renew their benefits while the programme exists.
'They want to take advantage'
The approximately 800,000 people protected under Daca are known as "Dreamers".
But on Twitter, Mr Trump said the programme was being misused by a growing number of illegal migrants and accused Mexico of being lax about border security.
He urged Republicans in Congress to pass "tough" new anti-immigration legislation.
Mexico is doing very little, if not NOTHING, at stopping people from flowing into Mexico through their Southern Border, and then into the U.S. They laugh at our dumb immigration laws. They must stop the big drug and people flows, or I will stop their cash cow, NAFTA. NEED WALL!— Donald J. Trump (@realDonaldTrump) April 1, 2018
Border Patrol Agents are not allowed to properly do their job at the Border because of ridiculous liberal (Democrat) laws like Catch & Release. Getting more dangerous. “Caravans” coming. Republicans must go to Nuclear Option to pass tough laws NOW. NO MORE DACA DEAL!— Donald J. Trump (@realDonaldTrump) April 1, 2018
Mr Trump's Sunday tweets referred to "caravans" coming, a possible reference to a travelling group of more than 1,000 migrants which had featured earlier on Sunday on Fox & Friends, known to be one of Mr Trump's favourite TV shows.
The mostly Honduran migrants, including whole families, are travelling together through Mexico to try to protect themselves against criminal gangs and harassment. Some say they will claim asylum once they reach the US border.
Mr Trump appeared once again to blame current illegal immigration on the Daca programme as he arrived for an Easter church service near his Mar-a-Lago resort in Florida.
"A lot of people are coming in because they want to take advantage of Daca and we're going to have to really see," he told reporters.
"They had a great chance, the Democrats blew it."
In his Sunday tweets and remarks to reporters in Florida, he also threatened to walk away from the North American Free Trade Agreement (Nafta).
What did Mexico say?
Mexico's interior minister said on Monday he had spoken to the US homeland security secretary Kirstjen Nielsen and they had agreed to work together to explore how to deal with the flow of migrants.
"We agreed to analyse the best ways to attend to the flows of migrants in accordance with the laws of each country," Interior Minister Alfonso Navarrete wrote in a post on Twitter.
Mr Trump's tweets come amid tense negotiations over Nafta between his administration and that of Mexican President Enrique Peña Nieto.
Mexico goes to the polls on 1 July to elect a new president.
Leftist front-runner Andrés Manuel López Obrador said his country and its people would not be the punch ball (or pinata) of any foreign government.
The conservative candidate, Ricardo Anaya Cortés, challenged Mr Trump to deal with security issues on his own side of the border.
"We understand that the United States government is worried about undocumented migration to the United States but we are also very concerned about the arms trade from the United States to Mexico," he said.
Mr Trump's tweets gained a mixed reception on Twitter - including criticism from his former rival for the Republican presidential nomination, Ohio Governor John Kasich.
What are the 'caravans'?
In a Sunday tweet, Mr Trump wrote: "Getting more dangerous. 'Caravans' coming."
The line could be in reference to migrants moving en masse from Mexico's southern border with Guatemala toward the US, organised by volunteers called Pueblos Sin Fronteras (People Without Borders).
The group counted 1,200 people in the caravan when they set off in late March for the month-long trek - which is more than 2,000 miles (3,220km).
About 80% of the migrants are Honduran, fleeing poverty and also unrest in the country after the contentious re-election of President Juan Orlando Hernández last year.
This morning the caravan, anticipating a long day walk, got up at 4am to beat the sun. pic.twitter.com/Pk8URSSHP4— Adolfo Flores (@aflores) March 30, 2018
Caravans have walked to the US border before. The organised groups are designed to offer protection to migrants from cartels and authorities who could harm or deport them.
But Pueblas Sin Fronteras were surprised by the turnout for this march. Last year's caravan had only about 450 migrants in it.
Despite the migrants being in the country illegally, Mexican authorities have done nothing to stop them.
Mexico has the absolute power not to let these large “Caravans” of people enter their country. They must stop them at their Northern Border, which they can do because their border laws work, not allow them to pass through into our country, which has no effective border laws.....— Donald J. Trump (@realDonaldTrump) April 2, 2018