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The Latest on the migrant caravan pushing toward the U.S. border (all times local):

4:30 p.m.

The Mexican Interior Ministry has said it would immediately deport Central American migrants who tried to "violently" breach the border with the U.S. just south of California and that it would reinforce the border.

Meanwhile, Homeland Security Secretary Kirstjen Nielsen said Sunday that U.S. authorities will continue to have a "robust" presence along the Southwest border and that they will prosecute anyone who damages federal property or violates U.S. sovereignty.

About 500 migrants who arrived in Tijuana by caravan marched toward the border to plead for the U.S. to speed processing of asylum requests.

The march, however, was dispersed by tear gas after some in the group tried to force their way into the U.S. The Mexican government described Sunday's events as "acts of provocation" that were "far from helpful" for the migrants' objectives.

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12:30 p.m.

Migrants approaching the U.S. border from Mexico have been enveloped with tear gas after a few tried to breach the fence separating the two countries.

U.S. agents shot the gas, according to an Associated Press reporter on the scene. Children were screaming and coughing in the mayhem.

On the U.S. side of the fence, shoppers streamed in and out of an outlet mall.

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12:15 p.m.

Central American migrants, mostly men, appear to be trying to breach the border crossing between Tijuana and California.

U.S. Border Patrol helicopters flew low overhead, while U.S. agents held vigil on foot beyond the wire fence. The Border Patrol office in San Diego said via Twitter that pedestrian crossings have been suspended at the San Ysidro port of entry at both the East and West facilities.

U.S. 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.