The organizers and lawyers identified the strongest asylum cases — about 200, most of them children — and encouraged those people to apply for protection, while suggesting that the remainder seek protection in Mexico or elsewhere in Latin America.
To qualify for asylum, applicants must prove that they have been persecuted or fear persecution based on their race, religion, nationality, political belief or membership in a particular group. People who request protection at an American entry point must submit to a screening by an asylum officer, called a credible-fear interview. If the officer finds the fear credible, the case is then referred to an immigration judge for a full hearing.
But until late Monday none of the asylum seekers among the caravan had been allowed by border officials to begin the process.
Migrants’ advocates had accused the Trump administration of engaging in brinkmanship for political gain at the asylum seekers’ expense.
In a statement late Monday announcing the resumption of asylum processing at San Ysidro, Customs and Border Protection officials explained that the number of undocumented people they can process at border crossings depended on a range of factors including the complexity of cases, translation requirements, detention space and the number of migrants.
“As in the past when we’ve had to limit the number of people we can bring in for processing at a given time, we expect that this will be a temporary situation,” the statement said.
During the delay, most of the migrants adopted mind-sets of hardened patience.
“Really, nobody’s said anything,” said Arnaldo Rivera, 40, who fled his native Honduras with his wife and five children after the family was threatened by a gang. They were among the migrants who were waiting outside the entrance to the border crossing on Sunday, eating donated food and using a nearby public bathroom.
The family had staked out a patch of the pedestrian plaza by spreading out a blanket and demarcating it with a few knapsacks containing their belongings.
“It could be this afternoon, it could be tomorrow,” he said, shrugging. “God has the last word.”
Late Sunday, local, state and federal authorities tried to persuade the migrants to decamp from the pedestrian plaza and spend the night in shelters. But in an act of communal defiance, the caravan’s participants elected to remain where they were. As the officials walked away, the migrants applauded and cheered.
“We’ve experienced a lot, and this isn’t going to stop us,” said Shannel Smith, 29, who fled gang violence in Honduras and is one of about 35 transgender migrants in the caravan.
Ms. Smith was part of a delegation of about 50 migrants who were selected by the lawyers and caravan organizers to approach the American border entry on Sunday afternoon and test the authorities’ claim that they had no capacity to process asylum petitions.
But no members of that group, many of them children, were allowed to pass through the gate. Some decided to remain there for much of the night, corralled behind metal barricades and huddled under blankets on the cold concrete ground, maintaining pressure on the American government.
More than 24 hours after they arrived, eight members were finally invited to step through the gate.