He has used it as justification to deploy National Guard troops, and his comments about it have further strained US relations with Mexico. Department of Homeland Security (DHS) Secretary Kirstjen Nielsen issued a statement declaring, "If you enter our country illegally, you have broken the law and will be referred for prosecution".
The group from Honduras, Guatemala and El Salvador arrived in Tijuana on buses over the past couple of days, and majority said on Saturday that they meant to seek legal asylum in San Diego. It can hold about 300 people at a time, and officials had been warning that it might fill up.
The asylum-seekers began the day with anticipation, traveling in red-and-white school buses under police escort to a beachfront rally in Tijuana, where a steel fence juts out into the Pacific Ocean. In a statement from U.S. Customs and Border Protection supplied to AP, officials have confirmed that the border crossing can take in additional people as space and resources become available. CBS News correspondent Errol Barnett reports.
Trump vowed last week to "stop" the caravan and Cabinet members said they would deliver a swift response.
A caravan of Central American migrants criticized by Trump is seeking asylum in the United States.
He also said: "We have to have borders and we have to have them fast...and we need the wall". "We've had exactly a month without sleeping in a bed", she said. US Customs and Border Protection (CBP) agents announced they had reached capacity and would not process the applications. About 50 supporters watched on the US side, where they were held about 20 yards away. Most of those seeking asylum are Honduran women and children, but some are from El Salvador.
"We're fighting so that people who already have kids together are recognized as a family", said Emma Lozano, a pastor for Familia Latina Unida, an immigrants' rights group based in Chicago, who performed the wedding ceremonies.
But US officials warned that there wasn't enough room to process a large group at San Ysidro and that many, if not all, could be turned back. "I don't believe it", Nicole Ramos told the Associated Press news agency.
The migrants were expected to claim they have a "credible fear" of returning to their home countries.
Pelicans in familiar, hostile territory for game one against Golden State
When asked what he expected to see from Davis in this series, teammate Jrue Holiday responded with a confident answer. Golden State, they weren't sure exactly how many days they needed to pack for on their trip to the Bay Area.
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. Attorney General Jeff Sessions has called them "a deliberate attempt to undermine our laws and overwhelm our system".
The caravan takes place each year to protect those seeking asylum from the widespread sexual assault, kidnapping and violence that immigrants face when traveling alone or in small groups.
"People who have a legitimate fear of persecution under USA law have a right to present their case", Rep. Zoe Lofgren, the top Democrat on the House subcommittee on immigration, said on Monday.
"All I want is a place where I can work and raise my son", the 36-year-old said. He said his wife and their daughter have been released from custody while their asylum claim is under review and are staying with family in SC.
"I ask God and the government to give me asylum", she said.
Alexandra Bachan, a private immigration lawyer from Oakland, California, who volunteered to provide legal services training for the group, said that families were informed they could initially be split in detention: grandparents could be separated from their family members, men from the female members of their family, and, in some cases, parents from their children.
Administration officials and their allies claim that asylum fraud is growing and that many who seek it are coached on how to do so. If they pass an asylum officer's initial screening, they may be detained or released with ankle monitors.
Fellow Honduran Wendi Yaneri Garcia is confident she will be released from the USA detention centre while her case is pending as she is travelling alone with her sick two-year-old son. She hoped to move in with a sister in San Francisco.
She said she fled her home in Jutiapa, Honduras, because the father of her son threatened to kill her and their child.