This weekend, about 2,000 of the migrants crossed into Mexico from Guatemala by fording the Suchiate River, after violent clashes with Mexican riot police who blocked a lot of them from crossing on a bridge.
Mexican police in riot gear shadowed the caravan's arrival along a southern highway but did not impede the migrants' journey.
On Saturday, Mexican authorities opened the border for women and children on the overcrowded bridge, taking them to a shelter in the city of Tapachula, about 40 kilometers from Ciudad Hidalgo. After Mexican authorities slowed access through the border bridge to a crawl, hundreds of migrants are boarding the rafts or wading across the river and crossing into Mexico illegally.
Hundreds of Honduran migrants decided on Saturday to cross the Suchiate River in their eagerness to reach the US.
The decision to form a migrant caravan came after some migrants have up trying to enter Mexico legally because the asylum application process was too slow and most consider the U.S.as their final destination is the USA, where Trump says he will close the border on them.
Trump also said he would start cutting off federal aid to Guatemala, Honduras, and El Salvador.
Mr Trump made the comment in a tweet saying the group includes "Criminals and unknown Middle Easterners".
The Associated Press reported Monday the size of the caravan has grown from about 200 people when it was first formed, to 4,000 when it entered Mexico and 7,000 as it pickup up steam through that country. "We're gonna keep on going and we're not gonna stop", Luis Puerto, 39, of Colon, Honduras, said in English.
Approximately 640 migrants requested asylum in Mexico, according to a statement from the Mexican government and the National Migration Institute obtained by CNN early Sunday morning.
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Migrants have commonly cited widespread poverty and gang violence in Honduras, one of the world's deadliest nations by homicide rate, as their reasons for joining the caravan.
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.
"They're not coming into this country", Trump added.
It's unclear exactly how many migrants were allowed to legally cross the border into Mexico, where they were taken to shelters to rest. Speaking to reporters on a tarmac, Pompeo accused the caravan of using women and children "as shields as they make their way through".
"We asked for people to give us rides, we sold the little we had to come", she added.
"They catch you, and you try to get back", said Imner Anthony Fuentes, a 29-year-old who reportedly was deported for the sixth time from the US five months ago.
"We thought the caravan was passive but there were unruly people, I was disappointed", said Gonzalo Martinez, a 37-year-old farmer, as he boarded a bus in Tecun Uman, Guatemala to take him back to Honduras. "We've not done anything against Mexican law".
Trump said "full efforts" were underway to halt the caravan's progress toward the United States.
More than 3,400 Hondurans migrants were returned to their home country over the weekend, according to a migrant assistance body.