“Wet foot, dry foot” policy that created a path to legal residency for thousands of Cubans was abruptly ended.
The immigrants, who arrived at Tijuana on Wednesday evening, are currently staying at two immigrant shelters, according to reports.
They are expected to be joined in the Mexican border city Tijuana by another 200 Central Americans in the coming days.
The caravan was organised by a group called Pueblos Sin Fronteras, Spanish for People Without Borders (PSF).
PSF has organised caravans for several years but this is the first that has attracted mainstream media coverage in the US, according to reports.
US lawyers are expected to hold clinics this week to explain what the immigrants should expect during their applications for asylum.
US President Donald Trump has called the immigrant caravan a sign of weak US law on migration and said it should be stopped in Mexico.
Kirstjen Nielsen, the secretary of homeland security, said in a statement on Wednesday regarding the immigrants that the US will enforce immigration law.
“If you enter our country illegally, you have broken the law and will be referred for prosecution. If you make a false immigration claim, you have broken the law and will be referred for prosecution,” Nielsen said.
In response, rights groups defended what they call a global right to apply for asylum.
Erika Guevara Rosas, the Americas director at Amnesty International, said in a statement: “Seeking asylum is not a crime in the USA or anywhere.
“The efforts of US officials to tarnish asylum seekers as criminals are cynical fabrications that ring hollow.”
The immigrants’ arrival comes the day after a third federal judge dealt a blow to the Trump administration’s efforts to end protections for undocumented immigrants brought to the US as children.
A judge ruled that the Deferred Action for Childhood Arrivals (DACA) programme, which paved the way for two-year renewable work permits for undocumented migrants brought to the US as children, must re-start after 90 days if the Trump administration cannot offer an explanation as to why it is illegal.
Trump ended the programme, which was created by an executive order in 2012 by former President Barack Obama, in September 2017.
Sarah Huckabee Sanders, White House press secretary, responded to the ruling on Wednesday, saying the “DACA programme violates federal law” and that the “judge’s ruling is extraordinarily broad and wrong on the law”.
Sanders said the ruling would encourage immigrants to come to the US border.