US Customs and Border Protection commissioner Kevin McAleenan said in a conference call with reporters that 69 migrants were arrested the previous day on the California side of the border.
Another nearly 1000 people ran through vehicle lanes or tried to cross illegally at other parts of the border, he said.
The volatile situation prompted US authorities to close the San Ysidro port of entry, the busiest crossing along the US-Mexico border, for six hours.
The migrant caravan has been camped out in Tijuana for the past two weeks.
It began as a few hundred people who convened at a bus station in San Pedro Sula, Honduras, more than a month ago and quickly swelled into the thousands as it marched and hitchhiked north through Guatemala and Mexico.
Mexican authorities say there are now more than 8000 migrants involved.
Many of them joined because travelling with a large group is a relatively inexpensive and safe way to cross Mexico, where migrants face many dangers from the drug cartels that control the human-smuggling trade.
Many of the migrants say they want to apply for asylum in the United States, but US border authorities are processing only a small number of asylum seekers per day, so frustration has grown.
That frustration bubbled over yesterday as a protest march by migrants turned into a chaotic scene, with people trying to breach the border fencing and US authorities using tear gas to repel them.
