Their numbers swelled to about 5,000 overnight and at first light they set out walking toward the Mexican town of Tapachula, 10 abreast in a line stretching approximately a mile.
It's not immediately clear where the additional travelers materialized from.
The Trump administration has characterized most US -bound Central Americans as economic migrants who have no legal standing to enter the United States.
They marched on through Mexico like a rag tag army of the poor, shouting triumphantly slogans like "Si se pudo!" or "Yes, we could!"
Maria Teresa Orellana, a resident of the neighborhood of Lorenzo handed out free sandals to the migrants as they passed.
After making it to the muddy banks of Mexico, she said, "No one checked my documents", as Consuelo headed to a taco restaurant.
Amid confusion over the numbers following Friday's chaotic scenes, a Mexican official said on Saturday that about 5,000 Hondurans were still waiting to enter Mexico from the Guatemalan side.
"They're not going to let us pass", said Julissa Hernandez, 16, who was aboard the tenth busload to head back toward Honduras from Guatemala.
Pompeo said he and Videgaray spoke of the importance of stopping the caravan before it reaches the US border. "I can do this", he said, pointing to the asphalt under his feet.
Earlier on Friday, Videgaray said the caravan had close to 4,000 people and that the migrants could individually present their claims to enter Mexico or seek refugee status.
The U.S. -Mexico border between Tijuana and San Diego is the world's busiest land border crossing.
Some, including 40-year-old Adriana Consuelo, paid raftsmen 25 pesos ($1.30) to ferry them across the river on vessels constructed of giant rubber tires.
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Mexican immigration agents occasionally circled the plaza in vans but did not move to detain the immigrants.
Sairy Bueso, a 24-year old Honduran mother of two, was another migrant who abandoned the bridge and crossed into Mexico via the river.
Among them was Osman Melgar, who nursed a bleeding gash on his shin, suffered when he fell as dozens of people packed on the bridge began fleeing when police, according to several eyewitnesses, used tear gas.
"In this way we confront the phenomenon of migration, because he who leaves his town does not leave for pleasure but out of necessity", said Lopez Obrador, who takes office December 1. Instead they accepted small groups for asylum processing and giving out 45-day visitor permits to some. Mexico has posted hundreds of extra police on the border. It released photos of migrants getting off buses at a shelter and receiving food and medical attention. They gathered in groups on the Mexican side, hoping to advance farther into Mexico at some point.
"One of my companions went to look for some plastic", she said.
"They're not coming into this country: They may as well turn back", Trump said Friday in Arizona. But "they are going to continue walking, and their feet won't heel as long as they keep walking", he said.
Juan Carlos Mercado, 20, from Santa Barbara, Honduras, says corruption and a lack of jobs in Honduras has stymied him.
"Look at these kids without diapers, without food", said Eva Fernandez, a USA citizen and California resident who heads an immigrant advocacy group, as she livestreamed the scene to friends in Honduras.
"Mostly, we left because there's no work" in Honduras, said Luis Pena, 43, who was among those crossing into Mexico on the river rafts and said he was bound for Los Angeles.
US President Donald Trump said on Sunday that his administration was doing all it can to prevent the migrant caravan from crossing the border into Mexico, warning that his government would not allow them to enter the US.
However, by the end of Thursday, Trump was also thanking Mexico for its efforts to contain the caravan. "They want to continue on their way". But as of this moment, I thank Mexico. "If that doesn't work out, we're calling up the military, not the National Guard".
Most of the migrants spoken to by Reuters said their ultimate goal was to reach the United States.