Migration is just as controversial in Mexico, where President-elect Andres Manuel Lopez Obrador said he will ask Mr. Trump to pony up more money to try to build Central American society and create jobs in Mexico, hoping to stem the flow of people to the U.S.
The migrants say that they are trying to escape violence and poverty.
Trump is threatening to call in the military to stop the migrants and is pressing for action by the U.S. Border Patrol, saying the caravan is a national emergency.
The majority of the new additions to the caravan in Mexico are migrants who previously entered the USA illegally but were deported, The Washington Post reported.
In six journeys, she rode the treacherous El Tren de la Muerte ("The Train of Death"), came into contact with drug cartels, and befriended numerous migrant families, many of whom never made it to the US.
Thousands of Central American migrants have continued to push forward in their attempts to reach the United States, despite efforts by Mexico to halt their advance. That was an apparent reference not only to the increasing prevalence of so-called sanctuary cities and states that shield illegal immigrants, but also to Congress' inability to agree on immigration reform or funding for his proposed border wall.
An earlier caravan in the spring led to the USA government amassing about 2,400 National Guard troops from four states near the southern border, although they are prevented by law from performing law enforcement duties or interacting with migrants.
Mexico's government has reportedly called on the United Nations to help with the 7,000-plus wave of Hondurans, whose numbers have almost tripled as the group broke through border gates to enter Mexico over the weekend.
"No one is capable of organising this many people", Mr Mujica said, adding that there are only two forces driving this: "hunger and death". The president also stirred controversy with a tweet that alleged criminals and unknown Middle Eastern had blended in with the refugees from Honduras, Guatemala, and El Salvador.
More than 7,000 people have joined the migrant caravan headed toward the U.S. border with Mexico, a United Nations spokesman said Monday, citing estimates of the International Organization for Migration.
Others lay exhausted in the open air, with only thin sheets of plastic to protect them from ground soggy from an intense evening shower.
"At least four journalists travelling with the caravan have said they've seen nobody from the Middle East or heard of anybody from the Middle East", wrote Dale.
President Trump expects the migrant horde to be turned before they reach the United States.
Under U.S. immigration law, the the United States can deny asylum if a person can be returned to a country where their life or freedom is not in danger, but only if the U.S. has entered into a bilateral or multilateral agreement that codifies the arrangement.
The Trump administration has pointed out a sharp decline in immigrant detentions in the first few months of this year as a vindication for the president's tough immigration policies.