Honduran President Juan Orlando Hernandez said he would meet Saturday with his Guatemalan counterpart Jimmy Morales to discuss the next steps in the crisis, which has triggered escalating anti-immigrant rhetoric from US President Donald Trump.
'The Democrats want the caravans, they like the caravans.
Migrants received help Sunday from sympathetic Mexicans who offered food, water and clothing. Hundreds of locals driving pickups, vans and cargo trucks stopped to let them clamber aboard.
The migrants, mostly from Honduras, say they are fleeing violence and poverty, and include women and children. There was no evidence of anyone being deported through such trickery, but the warnings made plenty leery of boarding, like Fidelina Vasquez, a grandmother traveling with her daughter and 2-year-old grandson.
The Mexican authorities had attempted to stop them at a border bridge between Mexico and Guatemala. "There is a lot of disorder", said Rivera, who was hoping to get on a bus back to Honduras laid on by the Guatemalan government.
They're not coming into this country. The country's interior ministry reported that on Friday, Saturday and Sunday a total 1,028 people had requested refugee status.
Trump has made it a political issue in the November 6 mid-term U.S. congressional election, threatened to cut off regional aid, close the U.S. -Mexico border and deploy troops there if Mexico failed to halt the migrants.
Trump blames the opposition Democrats for what he says are immigration laws and border policies that are not strong enough to protect the United States.
"We shall work with our partners in the region to investigate and prosecute to the fullest extent of the law all who seek to encourage and profit from irregular migration", she said.
President Trump threatened in a series of tweets on Thursday to "call up the USA military and close our SOUTHERN BORDER" if Mexico doesn't do anything to stop the flow of migrants moving north. The president has threatened to seal off the U.S. -Mexico border entirely, if necessary. "Today it's for them, tomorrow for us", Valdivia said, adding that he was getting a valuable gift from those he helped: "From them we learn to value what they do not have".
The Associate Press reports that the numbers swelled to about 5,000 overnight.
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The caravan is part of a tradition of mass migrations, often organised by advocacy groups, meant to provide safety in numbers to migrants, who face many threats to their safety along the perilous migrant trail. They walked in a line stretching about a mile.
Watch: Migrants break Guatemala-Mexico border fence on Friday. "No one will stop us, only God", he said.
Brenda Sanchez of San Pedro Sula rode in Valdivia's truck Sunday with three nephews aged 10 to 19. Nonw were detained when they made it to land.
As the migrants passed through villages on the outskirts of Ciudad Hidalgo, locals applauded, shouted encouragement and donated supplies.
"One of my companions went to look for some plastic", she said.
The migrants, who said they gave up trying to enter Mexico legally because the asylum application process was too slow, gathered Saturday at a park in the border city of Ciudad Hidalgo.
Mexican authorities have also said that federal and Chiapas state authorities were also providing assistance, like food, medicine, and medical treatment, as well as legal counselling.
Mexico's ambassador to Guatemala Luis Manuel Lopez told AFP the women and children would be processed by immigration authorities and taken to a shelter in the city of Tapachula, 40 kilometers (25 miles) away. "They've really stepped up, and it will not be forgotten".
Mr Trump, who has threatened to close down the United States border, said the military would be called upon if needed.
The migrants, who said they gave up trying to enter Mexico legally because the asylum application process was too slow and most want to continue to the US, gathered Saturday at a park in the border city of Ciudad Hidalgo.