U.S. authorities have reopened the San Ysidro border point of entry between San Diego and Tijuana, Mexico, after closing traffic in both directions in response to migrants trying to rush the border Sunday.

About 500 men, women and children overwhelmed Mexican police blockades, prompting U.S. agents to fire tear gas as U.S. Border Patrol helicopters flew overhead.

The Department of Homeland Security Secretary Kirstjen Nielsen said in a statement that the port of entry was closed "to ensure public safety in response to large numbers of migrants seeking to enter the U.S. illegally."

Mexico's Interior Ministry said in a statement that authorities were able to contain the group that "in a violent manner" tried to cross the border, and that those who are identified as participating would be immediately deported.

The statement said that in accordance with the Mexican government's policy of respecting human rights and the non-criminalization of migration, it would not deploy military forces to control the migrants, but that it would reinforce the border points where people tried to break through.

About 5,000 Central American migrants, many of them attempting to escape poverty and violence in their homelands, have arrived in recent days to Tijuana, just south of the western U.S. state of California, after making their way through Mexico via a caravan.

Earlier Sunday, U.S. President Donald Trump implored Mexico and Central American countries to halt the stream of migrants heading to the United States, even as Mexico denied his claim it was willing to allow U.S. asylum-seekers to stay there until their cases were decided by American immigration courts.

"Would be very SMART," Trump said on Twitter, "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 claimed opposition Democrats "created this problem. No crossings!" (VOA)

• A U.S. Customs and Border Protection officer walks along a wall at the border between Mexico and the United States, as seen from San Diego, California, Nov. 25, 2018.