The Border Patrol office in San Diego announced via Twitter that pedestrian crossings have been suspended at the San Ysidro port of entry at both the East and West facilities.
U.S. agents have shot tear gas at migrants after some tried to breach fence separating the two countries.
Bloomberg's TicToc posted video of the migrant caravan reaching the border as it was shut down Sunday.
President Donald Trump took to Twitter again Sunday to express his displeasure with the caravans in Mexico.
"Would be very SMART if Mexico would stop the Caravans long before they get to our Southern Border, or if originating countries would not let them form (it is a way they get certain people out of their country and dump in U.S. No longer)," he wrote.
Some Central American migrants, mostly men, tried to breach the border crossing between Tijuana, Mexico and California on Sunday, after pushing past a blockade of Mexican police standing guard near the international border crossing in a bid to pressure the U.S to hear their asylum claims.
Mexico's Milenio TV showed images of at least a few of the hundreds of migrants at the border tried to jump over the fence separating the two countries.
The migrants carried hand-painted American and Honduran flags and chanted: "We are not criminals! We are international workers!" The group mostly consisted of men, although some women pushed small children ahead in strollers.
U.S. Border Patrol helicopters flew overhead, while U.S. agents held vigil on foot beyond the wire fence in California.
More than 5,000 migrants have been camped in and around a sports complex in Tijuana after making their way through Mexico in recent weeks via caravan. Many hope to apply for asylum in the U.S., but agents at the San Ysidro entry point are processing fewer than 100 asylum petitions a day.
Some of the migrants who went forward Sunday called on each other to remain peaceful.
They appeared to easily pass through the Mexican police blockade without using violence.
A second line of Mexican police carrying plastic riot shields stood guard outside a Mexican customs and immigration plaza, where the migrants were headed.
That line of police installed tall steel panels behind them outside the Chaparral crossing on the Mexican side of the border, which completely blocked incoming traffic lanes to Mexico.
Irineo Mujica, who has accompanied the migrants for weeks as part of the aid group Pueblo Sin Fronteras, said the aim of Sunday's march toward the U.S. border was to make the migrants' plight more visible to the governments of Mexico and the U.S.
"We can't have all these people here," Mujica told The Associated Press.
Tijuana Mayor Juan Manuel Gastlum on Friday declared a humanitarian crisis in his border city of 1.6 million, which he says is struggling to accommodate the crush of migrants.
As hundreds of Central American migrants massed at the border intending to apply for asylum in the United States, all border traffic was halted Sunday at the busy crossing between San Diego and Tijuana, Mexico, the U.S. Customs and Border Protection agency said.
© Copyright 2021 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.