Members of the 6,000-strong caravan, mostly migrants from Honduras, have been sleeping outdoors, on cold floors or on mats in an overcrowded shelter since they arrived in Tijuana city across the border from San Diego, California, three weeks ago.
Mexican immigration authorities on Thursday began transporting some of the migrants via buses to a new shelter to help lessen the strain.
Under the harsh immigration policies introduced by the administration of President Donald Trump, U.S. border officials say they may have to stay put in Mexico for months before they can petition the authorities.
U.S. customs and border control officers fired tear gas canisters into Mexico at dozens of migrants who tried to rush border fencing on Sunday.
On Thursday, as a steady rain fell and partially flooded the sports complex serving as the main shelter, it was Mexican police who stopped more than a dozen migrants from the caravan approaching the nearby El Chaparral border crossing.
