Officials in the Mexican city of Tijuana say they have a humanitarian crisis on their hands.
Homeland Security officials have said as many as 600 people in the caravans have criminal records, but have not specified how they know, or given many details.
Authorities and residents in Tijuana are concerned the migrants might try to make another mass rush across the border.
Some Central American migrants, mostly men, tried to breach the border crossing between Tijuana, Mexico and California on Sunday, after pushing past a blockade of Mexican police standing guard near the global border crossing in a bid to pressure the U.S to hear their asylum claims.
Customs and Border Protection acknowledged that no charges were filed but declined to say why. The mayor, who supports the deportation of violent migrants, once again called on the federal government and the newly elected leader to step up their efforts to support the city, which is struggling to accommodate around 8,000 migrants now waiting for the U.S. to process their asylum claims.
A U.S. Border Patrol agent stands on the U.S. side of the border, seen through the border structure from the Mexican side where the border meets the Pacific Ocean, Friday, Nov. 16, 2018.
Tough stance on caravan keeps criminals in Mexico
Irineo Mujica, who has accompanied the migrants for weeks as part of the aid group Pueblo Sin Fronteras, said the aim of Sunday's march toward the US border was to make the migrants' plight more visible to the governments of Mexico and the U.S.
Experts had expressed concerns about unsanitary conditions at the sports complex where more than 6,000 migrants are packed into a space adequate for half that many people.
Approximately 7,000 migrants remain on the Mexican side of the border demanding to be let into the United States.
Officials say it appeared most of the rocks were thrown from the Mexico side and no one was charged on the USA side with assaulting the agents.
Central Americans are typically turned over to ICE, which flies them back home.
Hundreds of the migrants are now living in hastily erected tents in Tijuana hoping to be able to cross into the U.S.to claim asylum - and then wait for their claims to be adjudicated by immigration judges. One of those other agents used a Taser to subdue Rodriquez, who was detained, arrested and charged in U.S. District Court later that day on one count of assault on a federal officer and one count of alien in possession of a firearm.