"We do not have the necessary and sufficient infrastructure to fully attend to these people to give them a decent space", Gastelum said at a press conference, adding that he will not pay for the migrants' stay in the city with the money intended for the locals.
"Migrants at the Southern Border will not be allowed into the United States until their claims are individually approved in court", he tweeted. He tweeted, "our very strong policy is Catch and Detain". Trump said on Twitter.
Hours earlier, The Washington Post quoted her as saying that the incoming administration of Andres Manuel Lopez Obrador had agreed to allow migrants to stay in Mexico as a "short-term solution" while the USA considered their applications for asylum.
Mexico's incoming interior minister Olga Sanchez Cordero was quoted by the Post as confirming the agreement during an interview with the newspaper, but on Sunday her office issued a statement denying any deal.
Under a "safe third" agreement, the USA could force migrants to seek asylum in Mexico.
President Donald Trump on Saturday announced migrants seeking asylum in the United States via its southern border would need to wait in Mexico while their claims are processed, appearing to confirm a report regarding a new bilateral deal.
In Tijuana, numerous migrants who are fleeing violence and poverty are seeking asylum in the United States and face the prospect of spending months in the border city before they have the opportunity to speak with a USA official.
She said she was considering accepting Mexico's offer to stay and work in Chiapas as a refugee.
Image Central American migrants mostly from Honduras aim to reach the US in hope of a better life
Trump used the caravans as an election issue in this month's midterms, sending USA military to the border and authorising troops to use lethal force.
Migrants from poor Central American countries moving towards the United States in hopes of a better life, walk along the road between Zapopan and Tequila in the Mexican state of Jalisco, on their trek north, on November 13, 2018. President Trump is claiming, without evidence, that "it is a way they get certain people out of their country and dump in U.S".
Many are hoping to apply for asylum in the USA - but agents at the San Ysidro entry point are processing fewer than 100 asylum petitions a day.
Several hundred Central American migrants, mostly men, had pushed past a blockade of Mexican police near the crossing, seeking to pressure the United States to hear their asylum claims.
Most of the migrants are camped inside a sports complex, where they face long wait times for food and bathrooms.
Tijuana Mayor Juan Manuel Gastlum on Friday declared a humanitarian crisis in his border city of 1.6 million, which he says is struggling to accommodate the crush of migrants.
No information was available on whether the woman was planning to claim asylum in the US.
Because the regular border crossings were closed, the migrants headed for the cargo area where the railroad crosses, Alvarez said.