All border traffic was halted on Sunday at the busy crossing between San Diego and Tijuana, Mexico, the U.S. Customs and Border Protection agency said, as hundreds of Central American migrants massed at the border intending to apply for asylum in the United States.

Traffic in both directions has been suspended at the San Ysidro port of entry, the agency said on Twitter.

In a statement, U.S. officials said that the Customs and Border Protection "had deployed additional personnel to the San Ysidro port of entry on Sunday. As the demonstrations on the Mexican side reached the border area, some members of the demonstration split off to head towards multiple locations along the border. Some attempted to enter the U.S. both directly east and west of the border crossing.

The agency added that "these attempts to illegally enter the U.S., and the response to them continue. Some attempted to illegally enter the U.S. through both the northbound and southbound vehicles lanes at the port of entry itself. Those persons were stopped and turned back to Mexico."

U.S. President Donald Trump has raised alarms about the caravan of migrants as it approached the United States, and has deployed military forces to the border to support the Border Patrol.

--CNBC contributed to this article.