The remaining 400 or so members of the caravan now face hard choices: whether to cross illegally into the United States, ask for asylum at the border or try to remain in Mexico.
A group of roughly 200 people, mostly Central Americans, has arrived at the U.S. -Mexico border seeking political asylum.
"We have reached capacity at the San Isidro port of entry", said Customs and Border Patrol (CBP) Commissioner Kevin McAleenan in a statement on Sunday, adding that the immigrants "may need to wait in Mexico".
After the migrants arrived at the port, organizers huddled with American lawyers to discuss a plan, then sent a group of about 100 migrants through the entrance gates of the port. Those who weren't processed by US authorities would wait and could use the time in Tijuana to gather evidence to support their asylum claims, said Irineo Mujica, the director of Pueblo Sin Fronteras, a migrant rights group that organized the caravan.
According to the Associated Press, U.S. immigration lawyers are telling caravan participants who traveled through Mexico to the border with San Diego that they face possible separation from their children and lengthy detentions. Most of those seeking asylum are Honduran women and children, but some are from El Salvador.
Almost 80 percent of asylum-seekers passed the initial screening from October through December, the latest numbers available, but few are likely to eventually win asylum.
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Numerous caravan members have said they are fleeing death threats by local gangs, retaliatory rape and political persecution in their native countries, which include Honduras, Guatemala and El Salvador.
If they eventually succeed in entering US custody, the migrants will be at the beginning of a perhaps longer and more complicated journey through the immigration court system, where the odds will be stacked against them. Many are fleeing violence in their home countries and will ask the US for asylum.
Trump made a similar threat in March to push for changes in immigration law that he says would prevent criminals from entering the country.
Is this caravan something new?
The effort was organized by Pueblos Sin Fronteras, translated from Spanish as People Without Borders, which is not the same group as the Washington-based non-profit that provides computer classes to worldwide residents of the District of Columbia.
Asylum seekers are often released to family in the USA but some don't have any and seek sponsors.
Caravans like these have been gathering and travelling for some 10 years. Many have already done that, at one point the caravan drew up to 1,000 people as it crossed Mexico.
Central Americans in a caravan of asylum seekers that traveled through Mexico to the border with San Diego are receiving final information before they turn themselves in to US authorities.
President Trump says these families are putting the United States in peril.
Some Twitter users were quick to gibe at Trump's words about the closure of the country, calling for his impeachment, while others supported his drive to build the wall. Attorney General Jeff Sessions has called them "a deliberate attempt to undermine our laws and overwhelm our system".
"Mexico has the absolute power not to let these large "Caravans" of people enter their country". Asylum seekers are typically issued work permits while they wait for their cases to be adjudicated.
Trump was speaking in Washington Township, Michigan, at the same time that the White House correspondents' dinner was taking place back in Washington, DC, with some lawmakers and current and former members of his administration in attendance. The president dispatched the National Guard to the border shortly after railing against the group of migrants.