At least one migrant from Honduras was killed after being dropped by a vehicle, Honduran President Juan Orlando Hernandez told reporters after meeting with his Guatemalan counterpart.
"What we have seen in recent days is without precedent," said.
At one point on Saturday, several dozen migrants sang the Honduran national anthem on the edge of the muddy Suchiate River between Tecun Uman, Guatemala, and Ciudad Hidalgo, Mexico, on the desperate northward migration.
Others, including a middle-aged woman and her three children, lowered themselves from the bridge on a ladder and climbed onto a makeshift raft that provided them to Mexico while federal police were watching nearby.
Exhausted migrants waded across the searchiate, holding their belongings over the chest-high waters. Others brought rafts to Mexico.
A group of men helping the migrants across the river sang "Si se puede" in Spanish or "Yes you can". Occasionally, young men jumped from the bridge into the river while the crowd cheered.
Once in Mexico, the migrants rested in a nearby warehouse, which was converted into a shelter. There they received food, water and medical care.
Their journey continued one day after defiant caravan members rushed past border gates just to be stopped by ranks of Mexican riot police dispersing tear gas and smoke cans into the crowd.
The slow procession in the north has led to President Donald Trump threatening to cut aid to the Central American states and send troops to the US border should Mexico not stop the surge.
After US Secretary of State Mike Pompeo and top officials met in the Mexican capital the night before, US State Department spokeswoman Heather Nauert said on Saturday that "Mexico is fully committed to a secure, safe and orderly migration. " 19659002] At a rally in Elko, Nevada, Trump attacked the Democrats, hinting that they wanted more caravans. He called the migrant situation "sad from both sides".
Members of the caravan of rhetoric from Washington appeared to be unaffected on the border between Mexico and Guatemala.
"Our message is that we are not criminals," said Orlean Herrera of Honduras. "We come here because we need a better life, that's why we're here."
Another man shouted, "Donald Trump is the Antichrist."
On Saturday morning, the bridge was swarming with men, women, teenagers and children. Some fainted from the heat.
The Mexican authorities began on Friday with a stream of migrants, beginning with women and children, through gates near the bridge to Tapachula, where they board buses for refugee camps.
Others sang and cheered, stormed or climbed over a steel gate on Friday until the riot police beat them back with tear gas and smoke canisters. Video showed coughing and crying migrants collapsed on the bridge. Several policemen and an indefinite number of migrants were injured.
It was unclear how many migrants would cross the border and how long this process would take. The Mexican authorities have stated that they would allow migrants to enter the country if they have valid visas or meet other requirements.
Leaders across the region have publicly called for them to return for days.
Pompeo: "This is an organized effort"
Four Mexican policemen were injured in the stalemate on the Mexican border, Pompeo said Friday
Before reporters on an asphalt in Mexico City, where he had met with leaders about the caravan and other things, Pompeo accused the caravan of using women and children "as shields if they come through."  "This is an organized effort to get through and Pompeo said
Pompeo said he had had a "good talk" with Mexican President Enrique Peña Nieto, and that the two countries were focusing collectively on the theme of the caravan, but "the Mexican government makes all decisions on how to tackle this. "
Peña Nieto called the confrontation a" unique incident "and said that the migrants' protocols the Mexican immigration authorities did not follow. He added that some migrants "attacked and even injured a number of unarmed members of the Mexican police before they were able to stop the violence."
"Mexico will not allow anyone to enter its territory in an unpredictable and even less violent way," he said Friday evening in a video statement posted on Twitter.
Peña Nieto said Mexican officials would continue to greet those traveling with the traveling caravan despite Friday's incident.
Trump, who has been criticizing the caravan with fiery tweets all week, reiterated his threat on Friday that if Mexico does not stop the migrants, it will take drastic action.
"If that does not work, we'll call the military, not the Guard, we're We call the military, and we'll have the military stationed," Trump said. "They do not come to this country, they might as well turn back."
Collision on the bridge
Members of the caravan gathered in the border town of Tecun Uman on Friday morning. They waited for hours in oppressive heat – with temperatures in the mid-'80s and 70% humidity – to pack the streets for blocks. [No19659002] Around noon, they poured through gates on the Guatemalan side of the border Friday, cheering and singing as they marched. Solemn air horns boomed on the way to the port of entry of Mexico.
When they reached a steel fence with padlock near the Mexican side of the bridge, the sheer number of migrants allowed them to break through.
The Mexican police have repulsed them. Hundreds of Mexican federal police sealed the border as drones and helicopters hovered over the crowd.
At least a dozen migrants jumped into the river.
Some of the migrants on the bridge said they had joined the caravan because they were desperate for work and had no choice.
Will you reach the US border?
Mexican authorities have not said if anyone is coming from the caravan
They have already explained how they wanted to respond to the group:
• Anyone with a valid visa can enter and travel freely to move freely.
• Anyone who wants to be recognized as a refugee or as a beneficiary of "supplementary protective measures" must do so individually. Those who do so are held "at a migration station" for up to 45 working days.
• Anyone who "enters in an irregular manner" will be "rescued and subjected to administrative procedures and will, if necessary, do so." be sent back to their country of origin in a safe and orderly manner.
This spring, when another caravan of Central American migrants entered Mexico, this policy allowed  The last caravan arrives weeks ahead of the midterm elections in the United States, where many Republican candidates have repeated the President's message on strengthening border security and combating illegal immigration.  19659037] Trump has the caravan as a key theme in the upcoming Wah len and described the approach of the group as an attack on the US border. Immigration attorneys have accused his government of creating a crisis to motivate its electorate base
Honduran and Guatemalan leaders speak
Hernandez met his colleague Jimmy Morales on Saturday in Guatemala for work on " Implementing a strategy and logistics for the return of Honduran migrants, "Hernandez said on Twitter.
Hernandez also asked for permission from Guatemala to send civilian personnel to Honduran migrants in Guatemala on Friday, after several posts on his official
In addition, Hernandez requested permission to "land transport for those who want to return to He even thanked the Guatemalan government for "paying all our attention to our Honduran brothers."