Juan Manuel Gastelum, the city’s mayor, said on Friday he was requesting aid from the United Nations to help care for the 4,976 men, women and children who are currently living inside a sports complex.
City officials and volunteers are working together in Tijuana to assist the group, known as the migrant caravan.
The group left Honduras in mid-October and has been largely well-received through the towns and cities it passed through.
But, with the exception of Mexico City, the caravan never stayed for longer than two nights in any one location.
Many of the people in the caravan are fleeing violence and poverty and are seeking asylum in the US.
They now face the prospect of being stranded in Tijuana for months as they try to find US officials to speak to.
Manuel Figueroa, who leads Tijuana’s social services department, said city officials were bringing in portable toilets and showers, as well as shampoo and soap.
But officials said the supplies will not be enough.
“Because of the absence, the apathy and the abandonment of the federal government, we are having to turn to international institutions like the UN,” Mr Figueroa said.
Mr Gastelum, the mayor, has vowed the city’s public resources will not be used to deal with the situation.
On Friday, he said that the Mexican government claimed to have sent 20 tons of resources to Tijuana, but only 5 tons were for the migrants, while the rest was sent to secure the border.
Volunteers also had harsh words for the country’s leaders.
Rene Vazquez, a Tijuana resident who was volunteering at the stadium, said Mexico’s federal government ignored the problem by allowing the caravan to cross the country without stopping.
“I don’t have anything against the migrants – they were the most deceived, but this is affecting us all,” he said.
The migrants are also receiving support from local churches in Tijuana as well as from volunteers and private citizens, who are providing food.
Mexico’s Baja California state government is also on hand and said that 7,000 job openings had been identified for migrants who qualify.
It is uncertain whether many of the migrants will qualify for asylum in the US.
The Trump administration has spent weeks lambasting the caravan, which it said was filled with criminals, gang members and even – it insinuated at one point without any proof – terrorists.
Mr Trump also threatened on Thursday to shut down the border if his administration determined Mexico had lost “control” of the situation in Tijuana.
Some of the migrants have been left disheartened and exhausted after their journey.
Adelaida Gonzalez, who is from Guatemala City, arrived in Tijuana three days ago.
She said she was considering Mexico’s offer to stay in the country and work as a refugee.
“We would not have risked coming if we had known it was going to be this hard,” she said.
Additional reporting by agencies
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