The slow pace of legal processing prompting several thousands to cross the river illegally by raft or swimming, according to local officials and migrant organizers.
Seeking to maintain order after a chaotic Friday in which thousands rushed across the border bridge only to be halted by a phalanx of officers in riot gear, authorities began handing out numbers for people to be processed in a strategy seen before at US border posts when large numbers of migrants show up there.
Trump has made it a political issue in the November 6 midterm US congressional election, threatened to cut off regional aid, close the US-Mexico border and deploy troops there if Mexico failed to halt the migrants.
It was not immediately clear where the additional travellers had materialized from since about 2,000 gathered on the Mexican side Saturday night.
Many of them had spent more than 24 hours on the packed bridge where heat and hunger was adding to a growing sense of despair.
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.
Mr. Hernandez noted that migrants from elsewhere in the region had joined the caravan, along with others from "outside the region", though he did not cite specific nationalities.
On Saturday the Honduran Office of Foreign Ministry released a statement noting that it had closed the border with Guatemala at Aguas Calientes in order to "save the lives and physical integrity of citizens and foreigners" that try to pass through customs in this city. "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.
The day before, the Mexican authorities opened the border to women and children who were then taken to a shelter in the city of Tapachula, about 40 kilometres (25 miles) from Ciudad Hidalgo, Mexico.
Mexico had indicated their decision to detain and repatriate migrants who enter Mexico in violation of Mexican law, and in instances where migrants apply for asylum, process the requests in accordance with Mexican law. On the Mexican side of the bridge, they were met by Mexican police in riot gear.
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The leaders of all three countries have come under intense pressure from US President Donald Trump, who for days has warned that the caravan must be stopped.
Changes to detention rules saw thousands of migrant children detained and separated from their parents at the US-Mexico border earlier this year, sparking national and worldwide condemnation.
Some migrants have tried to avoid the border checkpoint in Ciudad Hidalgo, Mexico, by crossing the Suchiate river.
"Let's all walk together!" and "Yes, we can!" they said. It's the favorite - and only - toy of her two daughters, 4-year-old Victoria and 3-year-old Elisabeth, who trudged beside her gleaming with sweat.
On Saturday, Mexican immigration authorities only allowed some 640 migrants through the official border crossing on a bridge spanning the Suchiate River. Authorities handed out numbers for people to be processed in a strategy seen before at US border posts when dealing with large numbers of migrants.
US Department of Homeland Security Secretary Kirstjen Nielsen noted that her agency is monitoring the caravan while going so far as to suggest that the migrant movement can serve as a cover for transnational criminal organizations.
Changes to detention rules saw thousands of migrant children detained and separated from their parents at the US-Mexico border earlier this year, sparking national and worldwide condemnation. "There are risks that we must take for the good of our children".
In interviews along the journey, migrants have said they are fleeing widespread violence, poverty and corruption in Honduras.