TIJUANA, Mexico — For the past month, the Central American migrant caravan has been cared for by generous Mexicans who have donated food and shelter for the thousands slowly making their way north to the U.S. border.

Now that the caravan has arrived in Tijuana, a city of immigrants itself, the reception has been noticeably cooler. On the U.S. side, Marines have been fortifying the border with extra barbed wire, and U.S. authorities have warned that they won’t allow large groups of migrants to enter. On the Mexican side, Tijuana’s mayor has referred to the migrants as “bums” and a “horde,” and a small group of residents held a protest Sunday morning shouting “No to the invasion!” and “They are terrorists!”

Jaime Malacara, 48, who works in private security, joined several dozen others at a traffic circle to express dismay at the caravan. He fears that the thousands of Central Americans who have arrived include bad people who will hang around and increase crime in an already violent city.

“Imagine if many of those bad guys — not all are bad, but some bad — start making gangs here?” Malacara said. “Those who break the law shouldn’t be here.”

The protest took place at a statue of Cuauhtémoc, an Aztec ruler, and participants appeared to be outnumbered by the dozens of journalists from around the world who have converged here to monitor the progress of the caravan. The residents at the protest mostly worried about rising crime, a possible confrontation with the United States, and how more caravans might follow if this one is allowed to pass.

“We’re against uncontrollable migration,” said Edgar Martínez, 42, a teacher and dual U.S.-Mexican citizen.

He said he feared that the caravan would eventually try to push its way across the border, prompting the United States to shut down the legal crossing that many in Tijuana rely on for daily work and errands.

“If they bumrush, they’re going to close the border. That is going to affect the people here,” Martínez said. “We wait up to three hours to cross the border sometimes. We don’t want it to become six.”

Across town, residents who support the migrants and their right to apply for asylum in the United States held a gathering.

For the past week, members of the caravan have been trickling into Tijuana, taking shelter at a sports complex abutting a highway and the border fence. Volunteers from church groups and others have given food and medicine, and entertained the migrant children by singing songs and making balloon animals.

Mayor Juan Manuel Gastélum has been less supportive. He has described the influx of migrants as a problem for Tijuana and dismissed the claim that many are fleeing violence and political persecution.

“Human rights should be reserved for righteous humans,” Gastélum said last week.

President Trump seized on the mayor’s comments in a tweet on Sunday, writing: “The Mayor of Tijuana, Mexico, just stated that ‘the City is ill-prepared to handle this many migrants, the backlog could last 6 months.’ Likewise, the U.S. is ill-prepared for this invasion, and will not stand for it. They are causing crime and big problems in Mexico. Go home!”