President Donald Trump has vowed to send the US military to secure the nation’s southern border with Mexico.
“We are going to be doing things militarily,” Mr Trump said at the White House on Tuesday, adding that it would be a “big step”.
Earlier Mr Trump threatened to cut aid to Honduras amid reports of a “caravan” of asylum seekers heading for the US.
Both of Mr Trump’s predecessors in the White House deployed National Guard troops to help secure the US border.
President Barack Obama sent hundreds of soldiers to guard the boundary, while President George W Bush deployed thousands of troops to help Border Patrol in what was called Operation Jump Start.
During a working lunch with leaders of Baltic countries on Tuesday, Mr Trump told reporters the North American Free Trade Agreement (Nafta) was at risk unless Mexico stopped the flow of migrants.
Earlier in the day, he tweeted for the third day about the “caravan” of migrants heading north from Central America.
“The big Caravan of People from Honduras, now coming across Mexico and heading to our ‘Weak Laws’ Border, had better be stopped before it gets there,” he tweeted.
“Cash cow Nafta is in play, as is foreign aid to Honduras and the countries that allow this to happen.”
Mr Trump first began tweeting on Sunday about the “caravan” of nearly 1,000 undocumented immigrants, following a Fox News report that used the term.
The group, which has been marching along roadsides and railways in the southern Mexican state of Oaxaca, is being organised by Pueblo Sin Fronteras (People Without Borders).
The president has been tweeting about illegal immigration for the last few days, accusing Democrats of allowing “open borders, drugs and crime”.
This is not the first time that Mr Trump has criticised Honduras, which has been plagued by increasingly deadly unrest since a disputed presidential election last November.
During a meeting at the White House in the Oval Office in January, he reportedly referred to the Central American nation as a “shithole”.
When is Trump going to build his wall?
Constructing a “big, beautiful wall” along the Mexican border was a signature campaign promise for Mr Trump, but so far the plan to erect a new physical barrier has been thwarted by lawmakers and appears to have stalled.
A major government spending bill which he signed last month to fund the federal government included just $1.6bn in border wall spending.
That fell far short of the $25bn the White House had sought – and there were strings attached to the funding Congress did approve.
Most of it can only be used to repair stretches of the 1,900 mile (3,100km) border where there already is a wall, not to build new segments.
Last month the Pentagon confirmed that Mr Trump held “initial” talks with Defence Secretary James Mattis about using some of Pentagon’s budget for constructing the wall.
Two Democratic US senators wrote to the Pentagon chief on Monday saying that “the Department of Defense has no legal authority, with or without a reprogramming request, to use appropriated funds for the construction of a border wall”.
“Such a controversial move could only be funded by cutting other vital priorities for our service members,” wrote Senators Dick Durbin and Jack Reed.