Authorities are preparing for an influx of migrants, with local police chief Gerardo Hernandez saying that five shelters had been set up in Ciudad Hidalgo to accommodate up to 4,000 people.
Numerous migrants are seeking refugee status in either Mexico or the United States.
"If that doesn't work out, we're calling up the military, not the guard, we are calling up the military and we're going to have the military stationed there, not coming into this country". "We just want to move ahead with our lives", he said Sunday.
"We are imprisoned here, like animals". Once they file a claim, they can go to a shelter to spend the night.
Mexican President Enrique Pena Nieto described the situation as "unprecedented".
"A lot of people say 'I wonder who started that caravan?'" he said. Waving a Honduran flag to cheer on the migrants, he didn't seem particularly anxious about Mexican immigration authorities.
Mexico's interior secretary, Alfonso Navarrete Prida, denounced violence and acts of "provocation" by some of the migrants in the caravan and vowed that Mexico would respect the rights of those seeking entry into Mexico. Honduras, for example, suffers from a homicide rate of 43 per 100,000 citizens.
But the slow pace frustrated those stuck on the bridge, where conditions were hot and cramped, and some pleaded at the main gate: "Please let us in, we want to work!"
Despite warnings to turn back this week from US President Donald Trump, one migrant, Erasmo Duarte, from Honduras, said before the journey: "We are going to reach the United States".
The border post is guarded by a heavy security force and tall metal gates.
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Chanting "Yes we can!" and "Mexico!" About 640 migrants have requested asylum in Mexico and 2,200 remain camped on a bridge connecting Guatemala and Mexico, according to statements by the Mexican Government. Men and women, some with young children and babies drenched in sweat, began storming and climbing the barrier - tearing it down.
"We are about law and order and borders and jobs, and they are about allowing crime to enter our country with open borders".
After an emergency meeting in Guatemala, the presidents of Honduras and Guatemala said an estimated 5,400 migrants have entered Guatemala since the caravan was announced a week ago and about 2,000 people have returned voluntarily to Honduras.
Back in Honduras, hundreds marched in the capital Tegucigalpa in solidarity with their compatriots.
On Thursday, Trump branded the migrants an "onslaught" and an "assault on our country" in a series of typically fiery tweets.
He has also threatened to cut aid to Honduras, Guatemala and El Salvador.
"We don't yet know if we will make it to the (U.S.) border, but we are going to keep going as far as we can", said Rodrigo Abeja, one of the migrants' leaders, adding that they would strike out Sunday morning for the city of Tapachula.
Mexican Foreign Minister Luis Videgaray insisted Mexico would not cave to pressure to detain the migrants, urging the Trump administration to address the root causes of their northward flight: violent crime and poverty.
The soft-spoken 25-year-old said he was travelling with three friends who chose to remain in the caravan, but that for him, the fear of being deported once he reached Mexico was too much.
Since his campaign days, Mr Trump has lambasted illegal immigrants, and this latest caravan comes after a major immigration crackdown.