Despite Mexican efforts to stop them at the Guatemala-Mexico border, about 5,000 Central American migrants resumed their advance toward the US border Sunday in southern Mexico.
Dressed in riot gear, police arrived along a southern highway in several buses, ahead of the throngs of men, women and children marching north after they crossed the Guatemalan border.
"We're just making sure they pass safely and then we'll steer them" to a migrants shelter outside the city centre of Tapachula, about 32 kilometres north-west of the border, he said.
On Saturday, Mexican immigration authorities only allowed some 640 migrants through the official border crossing on a bridge spanning the Suchiate River.
Numerous migrants, the overwhelming majority fleeing violence and poverty in Honduras, slept on the bridge through heavy rain overnight, dozens of them crammed against a metal border gate guarded by Mexican police.
Trump also expressed frustration with Mexico's military and police, saying they appear "unable to stop the Caravan" and that he has alerted the U.S. Border Patrol and military to what he termed a national emergency.
The numbers of migrants that started out from Honduras last week have quickly swelled to as many as 7,000, the Los Angeles Times reported.
Numerous bedraggled travelers of the swollen caravan appeared determined to keep moving, saying they are fleeing a toxic mix of violence, poverty and endemic corruption and would not turn back.
Group leaders said the caravan, which will be smaller than the original one, would strike out Sunday morning for the city of Tapachula.
The caravan members ranged from farmers and bakers to housewives and students, and included a whole block of friends and family from the Honduran city of El Progreso.
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Mexican President Enrique Pena Nieto said in a late Friday night address to his fellow citizens that a large group of migrants had "tried to enter Mexican territory irregularly, attacking and even hurting some elements of the Federal Police", CBS News said.
Many say they are fleeing economic distress and violence in their homelands.
"They're not coming into this country", he said. The Trump administration proposed steep cuts in aid to Latin America and the Caribbean in its very first budget - ranging from 20 to 40 per cent for most countries - but Congress rejected the plan, keeping funding relatively stable compared to previous years.
But some managed to cross into Mexico illegally by boat over the Suchiate river. The number, however, may be misconstrued since people have been joining and leaving the caravan daily.
"Please let us in, we want to work!" they entreated agents at the main gate.
Will that work at the USA southern border?
"Why would I want to go to the United States if I'm going to be persecuted" there as well, she said.
And according to global law, the USA can not deport asylum seekers without first determining the validity of their claim.
"So as of this moment, I thank Mexico", Trump said Friday at an event in Scottsdale, Arizona.
If a migrant in the so-called caravan does not apply for asylum or possess the proper documents to travel into Mexico, the United States will not recognize their claims for refugee status and will IMMEDIATELY return them to their home country.