ESCUINAPA, Mexico (CBS) — A caravan of thousands of Central American migrants is speeding its journey to the U.S. border, breaking up into smaller groups as buses and trucks carry some hundreds of miles in a day while others behind remain stranded.

Authorities have been struggling to deal with the first sizeable group of 357 migrants who arrived in the border city of Tijuana, Mexico, aboard nine buses. Tijuana’s head of migrant services said the group arrived Tuesday and immediately went to a stretch of border fence to celebrate.

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Cesar Palencia Chavez said authorities had offered to take the migrants to shelters immediately, but they initially refused, saying they wanted to stay together. But he said that after their visit to the border, most were taken to shelters in groups of 30 or 40.

Central American migrants -mostly Hondurans- moving towards the United States in hopes of a better life, cross a street in Tijuana, Mexico, on November 13, 2018. (credit: GUILLERMO ARIAS/AFP/Getty Images)

On Tuesday, the U.S. government said it was starting work to “harden” the border crossing from Tijuana to prepare for the arrival of migrants. Customs and Border Protection (CBP) announced it was closing four lanes at the busy San Ysidro and Otay Mesa ports of entry in San Diego, California. It said the closures were needed “to install and pre-position port hardening infrastructure equipment in preparation for the migrant caravan and the potential safety and security risk that it could cause.”

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On Thursday, 1,100 Marines from Marine Corps Base Camp Pendleton in California were deployed to support border security, CBS San Diego affiliate KFMB reported. They were primarily tasked with installing concertina wire and pre-positioning jersey barriers, barricades and fencing.

Migrant caravans heading to the U.S. became a campaign issue in U.S. midterm elections. President Trump has ordered the deployment of over 5,000 military troops to the border and has insinuated without proof that there are criminals or even terrorists in the group.

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Many say they are fleeing rampant poverty, gang violence and political instability primarily in the Central American countries of Honduras, Guatemala, El Salvador and Nicaragua.