At that point, numerous marchers bypassed police by running across a dry riverbed.
But amid the stinging gas, several migrants turned back.
They appeared to get close to the border wall, Alvarez said.
USA border agents shot several rounds of tear gas after some migrants attempted to penetrate various points along the border and threw what appeared to be rocks at US authorities.
After the gas had cleared, Mexican federal police officers then pushed back the protesters from the area of the train crossing.
Homeland Security Secretary Kirstjen Nielsen said U.S. authorities will continue to have a "robust" presence along the southwest border and that anyone who damages federal property or violates American sovereignty would be prosecuted.
CBP added that some demonstrators "attempted to illegally enter the US through both the northbound and southbound vehicle lanes at the port of entry itself".
"After being prevented from entering the port of entry, some of these migrants attempted to breach legacy fence infrastructure along the border and sought to harm CBP personnel by throwing projectiles at them", Nielsen said.More news: Carlos Tevez: We are being forced to play Copa Libertadores
Video clips posted on Twitter showed large numbers of migrants dashing across a shallow concrete waterway toward the border.
President Donald Trump said the US will close its southern border with Mexico if needed, a day after USA agents shot several rounds of tear gas at migrants after some tried to breach a border fence.
President Trump then tweeted on Sunday morning, "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".
Mexico doesn't want the migrants any more than the US does. A federal judge has at least temporarily ruled against the policy, but the administration has taken steps to harden the border. The focus of the meeting immediately shifted to the day's crisis, and the political implications it might have for the treatment of migrants and the anti-migrant sentiment it might incite in Mexico.
Trump has repeatedly suggested without evidence that the migrant caravans are full of hardened criminals, but they are mostly poor people with few belongings who are fleeing gang violence.
Tijuana city officials say they have no money to improve conditions at the sports center, where more than 5,000 migrants are sheltering in a space with capacity for no more than 3,500. After being rebuffed, the situation grew more chaotic, with some migrants running across a dry canal and others trying to cross in different places.
The US president has deployed some 9,000 troops along the border in support of Customs and Border Protection agents.
"Now, I guess I'll just wait my turn, because I can't go back to my country", she said. A Washington Post report Saturday indicated that the USA and Mexico had come to a deal around such an arrangement, but in a separate report that followed, Mexican officials denied a deal had been made.