There were 10 buses and the drivers had been instructed to carry the migrants to shelters in Tapachula.
Since the convoy formed last weekend, Trump has threatened to halt aid to Honduras and Guatemala, and potentially close the USA border with Mexico with the help of the military if the migrants' march is not stopped.
Migrants travelling in a mass caravan burst through a Guatemalan border fence and streamed by the thousands toward Mexican territory on Friday, defying Mexican authorities' entreaties for an orderly crossing and U.S. President Donald Trump's threats of retaliation.
Mexican authorities said around 900 other migrants-tired of waiting on the bridge-resorted to crossing the Suchiate River below on makeshift rafts and police did not intervene as they clambered up the muddy riverbank on the Mexican side. The Mexican authorities accepted small groups for asylum processing and handed out 45-day visitor permits to others, reports the Associated Press.
"Full efforts are being made to stop the onslaught of illegal aliens from crossing our Souther (sic) Border".
"We are well aware that this country (Mexico) didn't receive us as we expected, and they can return us to Honduras, and we also know there are drug traffickers who kidnap and kill migrants", said Juan Flores, another migrant.
Hundreds of migrants have reportedly applied for refugee status in Mexico in Ciudad Hidalgo.
Just over two weeks before Election Day, it is nearly certain that Democrats and Republicans will be using the situation creeping towards the U.S.as fodder for their respective political campaigns.
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A Salvadoran government statement and the country's migration director, Herbert Hernandez, said about 100 of the Hondurans tried to enter "without going through the obligatory migration control" and soldiers and police took control of a border bridge between the two countries.
The Honduran president admitted however that social problems were a contributory factor: "Without a doubt, we have a lot to do so that our people can have opportunities in their communities".
The tweets came as Secretary of State Mike Pompeo prepared to embark on a tour of the region that will see him visit Mexico ahead of its December inauguration of President-elect Andres Manuel Lopez Obrador, as well as Panama.
Osman Melgar, who nursed a bleeding gash on his shin, suffered when he fell as dozens of people packed on the bridge began fleeing Mexican police using tear gas, according to several eyewitnesses.
They warned that anyone without papers would have to apply for refugee status or turn back, and anyone who crossed illegally would be detained and deported.
"I hope Trump allows us to make it to the other side", he said.
They are thought to be people who had been waiting on the bridge over the Suchiate River or in the Guatemalan town of Tecun Uman and who made a decision to cross during the night. "Change the immigration laws NOW!", he said. The entry into Mexico via the bridge has been closed.
Numerous migrants, the overwhelming majority fleeing violence and poverty in Honduras, slept on the bridge through heavy rain overnight, dozens of them crammed against a metal border gate guarded by Mexican police.
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In Guatemala, the migrants rose early and many left without eating breakfast, bound for Zacapa, the next city on their route.
The caravan has become a politically loaded issue, with only two weeks to go before the United States votes in key midterm elections, in which Trump is seeking to protect the Republican majority on Capitol Hill.
The caravan members ranged from farmers and bakers to housewives and students, and included a whole block of friends and family from the Honduran city of El Progreso.
Even though the goal is to reach the USA border, she said: "We only want to work and if a job turns up in Mexico, I would do it".
Of the approximately 5,400 migrants who set out from Honduras a week ago, some 2,000 have returned to Honduras but 3,000 more are continuing with their plan to get to the southern United States border.
The US President Donald trump said the actions of law enforcement in Mexico.
Ulises Garcia, a Red Cross official, said some migrants with injuries from their hard trek refused to be taken to clinics or hospitals, because they didn't want to leave the caravan. "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.
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