The decision to re-form the migrant caravan Saturday capped a day in which Mexican authorities again refused mass entry to migrants on the bridge.
Honduran President Juan Orlando Hernandez said he would meet Saturday with his Guatemalan counterpart Jimmy Morales to discuss the next steps in the crisis, which has triggered escalating anti-immigrant rhetoric from US President Donald Trump.
Many Central Americans in a mass caravan at the Mexican border with Guatemala appear inclined to apply for any kind of refugee status in Mexico, even though most initially meant to make it to the United States.
"Honestly, I want to get to the states to contribute to that country, to do any kind of work, picking up garbage", he said. It was unclear how numerous group were from the migrant caravan and how many were Mexicans who joined the march. They were not detained by the authorities upon crossing the border.
A caravan of Central Americans that formed in southern Mexico in late March also drew the ire of Mr. Trump, who on Thursday threatened to deploy the military and close the southern USA border if Mexico did not halt the latest procession.
More than 300 people have taken up a government offer of a bus ride home to their country, police said. Those attempting to skip the process would face deportation, but the size of the caravan will test Mexico, which has sought help from the U.N.to manage the issue.
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Mexico's federal government said on October 20 that almost "900 migrants" arrived in the country via unauthorized means.
The caravan of mainly Honduran migrants had surged through a series of police lines and barricades up to the final fence on Mexico´s southern border on Friday. "People have to apply for asylum in Mexico first, and if they fail to do that, the USA will turn them away", Trump wrote on his Twitter account on Sunday.
But many became impatient, and circumventing the border gate, swarmed across the river on rafts, swimming or wading in full view of the hundreds of Mexican police manning the blockade on the bridge.
"This is an organized effort to come through and violate the sovereignty of Mexico", Pompeo said.
Homan said on Sunday that the option of military intervention to protect the border is one that needs to be on the table.
Peña Nieto said Mexican officials would continue welcoming those traveling with the migrant caravan despite Friday's incident.
Meanwhile, Trump threatened to cut off aid to Honduras if they allow the march to continue. The Interior Ministry said in its statement that migrants will begin the refugee application process at the country's National Institute of Migration, where their data will be collected, before they are sent to shelters that have been "enabled for their accommodation". "They're not coming into this country".
Sairy Bueso, a 24-year old Honduran mother of two, was another migrant who abandoned the bridge and crossed into Mexico via the river.
"We are working to provide a peaceful and safe return trip and avoid that these movements keep happening in the future", said Mr Morales, who added that around 5,000 had amassed at the border seeking to enter Mexico.