The mayor of the Mexican border city increasingly under strain from the growing number of migrants arriving there in hopes of crossing into the U.S. says he expects funds supporting them to run out by Friday.

Tijuana Mayor Juan Manuel Gastelum revealed Tuesday the city only has enough resources to assist the crowds for a few more days. The city's treasurer, Ricardo Chavarria, told the San Diego Union-Tribune that Tijuana has been spending around $30,000 a day on the caravan arrivals.

“We won’t compromise the resources of the residents of Tijuana,” Gastelum said during a press conference. “We won’t raise taxes tomorrow to pay for today’s problem.”

Nearly all of the migrants that have arrived in Tijuana have been hunkering down at an outdoor sports complex within sight of the U.S. border -- a place that is becoming more overcrowded each day. A delegate in the Tijuana area and an official overseeing that shelter told Fox News on Wednesday there are currently around 6,000 migrants there, 4,000 of which are men. The rest are about split evenly between women and children.

Mexico’s new president Andrés Manuel López Obrador is set to begin his administration this weekend and Gastelum is hoping the federal government can step in and provide more resources.

A boy eats as others wait in line for dinner outside of a shelter housing members of the migrant caravan in Tijuana. (AP)

Obrador's government signaled Tuesday it would be willing to house the migrants while they wait to apply for asylum in the U.S., but did not elaborate on what plans it may be considering.

"Prepare ourselves to assume that a good part of them are going to be in this area of Mexico for the coming months," said the incoming foreign relations secretary, Marcelo Ebrard.

He vowed the government will “have to support local authorities,” according to the Associated Press.

"That is not a bilateral negotiation. That is something we have to do,” Ebrard said.

He also asked the Trump administration Tuesday to chip in at least $20 billion on development projects to help create jobs in Central America. Many of the migrants say they fled their home countries to escape threats of violence from gangs and to find work.

Chavarria told the San Diego Union-Tribune that Tijuana is in budget trouble because it's almost the end of the fiscal year and it does not want to cut back on municipal services.

"This is costing us... to keep these people here and all those funds have to come from someplace and it's municipal funds," Delegate Genaro Moreno, who represents the region, told Fox News.

Gastelum said the city is so starved for cash that it can’t afford extra tarps for the migrants ahead of the looming rainy Thursday forecast, the newspaper added.

Gastelum said officials have identified sites where the federal government can set up a facility to assist the migrants, but the outgoing administration has been silent in response.

“The pretext that they are leaving is not an excuse,” Gastelum said, according to the San Diego Union-Tribune. “I, as a citizen, want answers from this government that I pay taxes to.”