Trump begrudgingly signed a spending bill last month that provided far less money for the wall than he wanted.
He has been complaining that U.S. borders are too porous and immigration laws are too weak.
"Until we can have a wall with proper security, we are going to be guarding our border with our military".
"We can not have people flowing into our country illegally, disappearing, and, by the way, never showing up to court", Trump said. Mexico has said such "caravans" of mostly Central Americans, including many escaping violence in Honduras, have occurred since 2010.
Mexico's immigration authority told BuzzFeed that it plans to disband the caravan by Wednesday. "We have a meeting on it in a little while with General Mattis and everybody, and I think that it's something we have to do", Trump told reporters at a joint news conference with leaders of Estonia, Latvia and Lithuania. The White House did not immediately answer questions about Trump's tweets.
The Guard members were used for surveillance, communications, administrative support, intelligence, analysis and, in some cases, the installation of border security infrastructure.
Mexico's top presidential candidates launched their campaigns Sunday by attacking Trump, with the leftist front-runner saying his country is done being the United States president's "pinata".
Mexican officials intensified efforts to process the dwindling group and determine whether they had the right to stay in Mexico or be returned to their countries of origin.
In a 2011 interview with Bill O'Reilly on Fox News, Trump signaled interest in using the US military to stop illegal immigration. And this is from years ago; they still haven't recovered.
The statement begins: "We are a group of people from different nations, religions, genders, gender expressions, and sexual orientations migrating and seeking refuge".
Presidents Obama and George W. Bush both deployed National Guard troops at the border to help stop illegal immigration.
Active duty US troops were not used for the operation because there are prohibitions on using so-called Title 10 troops for law enforcement and similar duties within the United States. A group of about 150 men reportedly broke away and boarded a freight train after the caravan stopped, and could be trying to enter the U.S. But the rest stayed back and were unlikely to proceed until later this week. Republicans insisted that Obama "secure the border" before they would vote to overhaul the immigration system.
With conditions bad in Honduras following that country's hotly disputed November presidential elections, unexpectedly large numbers of people showed for this year's march. It is some 450 miles from the closest Central American country, Guatemala.