"I must, in the strongest of terms, ask Mexico to stop this onslaught - and if unable to do so I will call up the U.S. Military and CLOSE OUR SOUTHERN BORDER!" he said.
On Wednesday, the president also threatened to cut USA aid to the Northern Triangle countries - Honduras, Guatemala and El Salvador - saying "all payments made to them will STOP (END)!".
The president's warning echoes an earlier tweet on Wednesday, in which he again blasted Democrats for refusing to approve tighter border control and immigration laws.
Trump said that the immigration debate would be a "great midterm issue for Republicans", with November's elections less than one month away. Cooperating with the US on strict border policies has been met with a serious backlash in Mexico and contributed to the election of incoming-President Andres Obrador.
"We have today informed the countries of Honduras, Guatemala and El Salvador that if they allow their citizens, or others, to journey through their borders and up to the United States, with the intention of entering our country illegally, all payments made to them will STOP (END)!" he tweeted.
From about 160 people who departed last Friday from the Honduran city of San Pedro Sula, the migrants' ranks have ballooned as much as twentyfold, with estimates ranging as high as 3,000.
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Guatemalan President Jimmy Morales said Wednesday that while Central Americans are legally free to transit from country to country under a regional agreement, a "massive ingress of people without registering" puts Guatemala in a hard position because it's impossible to know who the people are and what may be the intentions of any of their leaders. It also comes as he seeks to mobilize his base ahead of November's midterm elections by portraying Democrats as aiding an "assault on our country" on immigration.
Mexico has sent hundreds of police to its southern border as a caravan of thousands of Central American migrants approaches from Guatemala.
"They should be locking them up as they enter Mexico from these Central American countries".
Arpaio was specifically addressing the caravan of several thousand reportedly transiting through Central America and heading toward the US border.
In April, Trump signed a proclamation to send the National Guard to the border to keep the migrants from entering the United States.
On Wednesday, an advance group of exhausted migrants reached Guatemala City where they took refuge in a church-sponsored shelter.
Update: The article was updated with information about President Trump tweeting a video of the caravan migrants receiving money. The trafficking networks are controlled by drug cartels and use drug-smuggling routes to help the migrants cross the USA border illegally.
He also slammed the leaders of Honduras, El Salvador and Guatemala for failing to intervene.