A previous attempt by a larger group of migrants to jump over the border wall was met with tear gas, sending women and children running back to the Mexican side.
A woman and two children were apprehended by USA border patrol agents shortly after they crossed into the United States from Mexico on Tuesday, Dec. 4.
Earlier, Karen Mayeni, a 29-year-old Honduran, sized up the fence while clinging to her three children, aged six, 11 and 12.
The Trump administration's fierce crackdown on the "migrant caravan" has caused the 6,000-strong group to stall in Tijuana, Mexico; with many choosing to return home rather than wait months for their asylum claims to be processed by American authorities.
Reuters reported that other migrants managed to squeeze through the fence on the beach. "We'll figure out what to do in a couple of days". Mexican authorities arrested and deported those they considered responsible for compromising the city's commitment to public order.
A young man sits on top of a building at a new migrant shelter on Sunday in an area known as El Barretal, in Tijuana, Mexico.
"We have a challenging and still potentially volatile situation in Tijuana".
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On Friday, Judge Jon Tigar refused to suspend his ruling, saying that the Department of Justice has not "rebutted the significant harms that will be suffered by asylum seekers with legitimate claims and the organizations that assist them", according to AP.
This problem, according to McAleenan, stems from weak immigration laws in the US leading migrant families to believe that they cross the border when they don't have valid asylum claims.
Applying for asylum at a border post can take months and with USA officials restricting the number of applicants to between 40 and 100 a day at El Chaparral port of entry in Tijuana, the migrants could be stuck for months or even years in the shelter.
U.S. Customs and Border Protection released surveillance video showing what looks to be two migrant children being handed over from the Mexico side of the wall into Arizona.
The commissioner added that these scenarios are being played out every day at the border. The ages of the two children who were dropped were unclear.
McAleenan said the United States was looking forward to working with the new president of Mexico to address the problem.