Tijuana Delegate Genaro Lopez Moreno slammed leaders of the migrant caravan in Mexico for selling false promises to those vying to enter the United States.

Moreno told Fox News' Griff Jenkins that caravan leaders "aren't coming through" on their promises of a "great American dream."

"[The migrants] are noticing that," he said. "They know they're gonna be better back home."

His remarks come as Tijuana Mayor Juan Manuel Gastelum said Tuesday that his city is running out of resources to help those in the caravan.

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Gastelum said he expects support funds to run out by the end of the week, and Treasurer Ricardo Chavarria said that the caravan is costing Tijuana around $30,000 each day.

The situation at the U.S.-Mexico escalated over the weekend, as thousands of migrants arrived at the border near Tijuana and the Mexicali area.

Central American migrants were reportedly throwing rocks and debris at Border Patrol agents, prompting them to fire off tear gas.

Luis Conde, a migrant from Guatemala with an American arrest record, told Jenkins that legal or not, he's heading to the United States.

"I don't go to the other side to do something bad," he said. "I go to work. And work is work -- here, there, anywhere."

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