Migrants hold American flags during a peaceful march. Most of the migrants in the group were men.
Stephanie Leutert, director of the Mexico Security Initiative at the University of Texas at Austin, described the Remain in Mexico plan as a strategy to take away the ability of migrants to live and work in the USA while cases are processed.
Authorities on the USA side used tear gas to disperse the would-be crossers, the journalists told CNN. The border crossing was temporarily closed after the brief skirmish. She ruled out that Mexico would become a "safe third country" for the migrants trying to reach the U.S.
Some saw an opportunity to breach the crossing.
Migrants were asked by police to turn back toward Mexico.
Honduran Ana Zuniga, 23, also said she saw migrants opening a small hole in concertina wire at a gap on the Mexican side of a levee, at which point USA agents fired tear gas at them.
"Children screamed and coughed". Fumes were carried by the wind toward people who were hundreds of feet away, not attempting to enter the U.S.
"We ran, but when you run the gas asphyxiates you more", Zuniga told the AP while cradling her 3-year-old daughter Valery in her arms.
Yards away on the USA side, shoppers streamed in and out of an outlet mall.
Rights groups have accused the US government of stalling the processing of asylum claims, allegations the US Customs and Border Protection denies. All northbound and southbound traffic was halted for several hours.
Demonstrators' show of solidarity came as U.S. Border Patrol agents fired tear gas at Central American migrants after as many as 500 people rushed police blockades on the Mexican side of the southern border in an apparent bid to cross into the U.S.
"As I have continually stated, DHS will not tolerate this type of lawlessness and will not hesitate to shut down ports of entry for security and public safety reasons", Nielsen said.
The policy, known as "Remain in Mexico", was formulated by the Trump administration to deal with the thousands of immigrants seeking asylum in the U.S.in the caravan.
The president is putting more pressure on Mexico, warning that he might close the southern border "permanently" if necessary.
"We can't have all these people here", Mujica said.
"Every once in a while, a new group gathers there, at the U.S. -Mexico border fence - and then pretty quickly after that, they are dispersed using tear gas".
One migrant from Honduras said, "They started throwing tear gas at us".
He also demanded that Congress fund his promised wall proposed for the border.
Meanwhile, Republican Senator Lindsey Graham of SC, took to Twitter to accuse critics of having to "really hate President Donald Trump to not understand the problems created by the caravans".
Mexico's Interior Ministry earlier said those identified as having tried to cross would be processed for deportation to their home countries. The Mexican government described Sunday's events as "acts of provocation" that were "far from helpful" for the migrants' objectives. President Enrique Pena Nieto offered thousands of Central Americans asylum on October 26 if they agreed to remain in southern Mexico.